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T. Monovasilis, T. Simos (2007)
New Second-order Exponentially and Trigonometrically Fitted Symplectic Integrators for the Numerical Solution of the Time-independent Schrödinger EquationJournal of Mathematical Chemistry, 42
H. Vyver (2007)
Phase-fitted and amplification-fitted two-step hybrid methods for y˝= f ( x,y )Journal of Computational and Applied Mathematics, 209
J. Vigo-Aguiar, T. Simos (2005)
Review of multistep methods for the numerical solution of the radial Schrödinger equationInternational Journal of Quantum Chemistry, 103
K. Tselios, T. Simos (2013)
OPTIMIZED FIFTH ORDER SYMPLECTIC INTEGRATORS FOR ORBITAL PROBLEMSRevista Mexicana De Astronomia Y Astrofisica, 49
T. Simos (2014)
An explicit four-step method with vanished phase-lag and its first and second derivativesJournal of Mathematical Chemistry, 52
T. Monovasilis, Z. Kalogiratou, T. Simos (2010)
Symplectic Partitioned Runge-Kutta methods with minimal phase-lagComput. Phys. Commun., 181
T. Monovasilis, Z. Kalogiratou, T. Simos (2007)
Families of third and fourth algebraic order trigonometrically fitted symplectic methods for the numerical integration of Hamiltonian systemsComput. Phys. Commun., 177
T. Simos (2012)
High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equationJournal of Mathematical Chemistry, 50
T. Monovasilis, T. Simos (2007)
Symplectic methods for the numerical integration of the Schrödinger equation, 38
Z. Kalogiratou, T. Monovasilis, T. Simos (2007)
A Fifth‐order Symplectic Trigonometrically Fitted Partitioned Runge‐Kutta Method, 936
G. Psihoyios, T. Simos (2006)
The numerical solution of the radial Schrödinger equation via a trigonometrically fitted family of seventh algebraic order Predictor–Corrector methodsJournal of Mathematical Chemistry, 40
M. Dong, T. Simos (2017)
A new high algebraic order efficient finite difference method for the solution of the Schrödinger equationFilomat, 31
I. Alolyan, T. Simos (2015)
A predictor–corrector explicit four-step method with vanished phase-lag and its first, second and third derivatives for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 53
C. Tsitouras, T. Simos (2002)
Optimized Runge-Kutta pairs for problems with oscillating solutionsJournal of Computational and Applied Mathematics, 147
T. Simos (2011)
A two-step method with vanished phase-lag and its first two derivatives for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 49
M. Chawla, P. Rao (1986)
phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
T. Simos, P. Williams (1999)
On Finite Difference Methods for the Solution of the Schrödinger EquationComput. Chem., 23
T. Simos (2004)
Exponentially - Fitted Multiderivative Methods for the Numerical Solution of the Schrödinger EquationJournal of Mathematical Chemistry, 36
T. Monovasilis, Z. Kalogiratou, T. Simos (2013)
Exponentially Fitted Symplectic Runge-Kutta-Nystr om methodsApplied Mathematics & Information Sciences, 7
I. Alolyan, T. Simos (2016)
An implicit symmetric linear six-step methods with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equation and related problemsJournal of Mathematical Chemistry, 54
T. Simos (2009)
A new Numerov-type method for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 46
Chen Tang, Wenping Wang, Haiqing Yan, Zhanqing Chen (2006)
High-order predictor-corrector of exponential fitting for the N-body problemsJ. Comput. Phys., 214
J. Vigo-Aguiar, T. Simos (2002)
Family of Twelve Steps Exponential Fitting Symmetric Multistep Methods for the Numerical Solution of the Schrödinger EquationJournal of Mathematical Chemistry, 32
F Hui, TE Simos (2016)
Four stages symmetric two-step P-stable method with vanished phase-lag and its first, second, third and fourth derivativesAppl. Comput. Math., 15
T. Simos (2009)
High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equationAppl. Math. Comput., 209
JD Lambert, IA Watson (1976)
Symmetric multistep methods for periodic initial values problemsJ. Inst. Math. Appl., 18
T. Monovasilis, Z. Kalogiratou, T. Simos (2006)
Trigonometrically fitted and exponentially fitted symplectic methods for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 40
K. Tselios, T. Simos (2004)
Symplectic Methods of Fifth Order for the Numerical Solution of the Radial Shrödinger EquationJournal of Mathematical Chemistry, 35
I. Alolyan, T. Simos (2015)
A high algebraic order predictor–corrector explicit method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equation and related problemsJournal of Mathematical Chemistry, 53
(2006)
Special issue — selected papers of the international conference on computational methods in sciences and engineering ( ICCMSE 2003 ) Kastoria , Greece , 12 – 16 September 2003 — preface
G. Herzberg, J. Spinks (1950)
Spectra of diatomic molecules
G. Avdelas, E. Kefalidis, T. Simos (2002)
New P-Stable Eighth Algebraic Order Exponentially-Fitted Methods for the Numerical Integration of the Schrödinger EquationJournal of Mathematical Chemistry, 31
T. Simos (2012)
Optimizing a Hybrid Two-Step Method for the Numerical Solution of the Schrödinger Equation and Related Problems with Respect to Phase-LagJ. Appl. Math., 2012
A. Konguetsof (2010)
A new two-step hybrid method for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 47
T. Simos, S. Arabia (2014)
On the Explicit Four-Step Methods with Vanished Phase-Lag and its First DerivativeApplied Mathematics & Information Sciences, 8
T. Simos (2013)
Accurately Closed Newton–Cotes Trigonometrically-Fitted Formulae For The Numerical Solution Of The Schrödinger EquationInternational Journal of Modern Physics C, 24
J. Dormand, P. Prince (1980)
A family of embedded Runge-Kutta formulaeJournal of Computational and Applied Mathematics, 6
D. Berg, T. Simos (2017)
High order computationally economical six-step method with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 55
T. Simos (2003)
New Stable Closed Newton-Cotes Trigonometrically Fitted Formulae for Long-Time IntegrationAbstract and Applied Analysis, 2012
Z. Anastassi, T. Simos (2007)
A Family of Exponentially-fitted Runge–Kutta Methods with Exponential Order Up to Three for the Numerical Solution of the Schrödinger EquationJournal of Mathematical Chemistry, 41
T. Simos, I. Famelis, C. Tsitouras (2003)
Zero Dissipative, Explicit Numerov-Type Methods for Second Order IVPs with Oscillating SolutionsNumerical Algorithms, 34
T. Monovasilis, Z. Kalogiratou, T. Simos (2016)
Construction of Exponentially Fitted Symplectic Runge–Kutta–Nyström Methods from Partitioned Runge–Kutta MethodsMediterranean Journal of Mathematics, 13
L. Ixaru, M. Rizea (1985)
Comparison of some four-step methods for the numerical solution of the Schrödinger equationComputer Physics Communications, 38
Fei Hui, T. Simos (2015)
A new family of two stage symmetric two-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 53
I. Alolyan, T. Simos (2016)
A new two stages tenth algebraic order symmetric six-step method with vanished phase-lag and its first and second derivatives for the solution of the radial Schrödinger equation and related problemsJournal of Mathematical Chemistry, 55
I. Alolyan, T. Simos (2016)
Family of symmetric linear six-step methods with vanished phase-lag and its derivatives and their application to the radial Schrödinger equation and related problemsJournal of Mathematical Chemistry, 54
Z. Kalogiratou, T. Monovasilis, G. Psihoyios, T. Simos (2014)
Runge–Kutta type methods with special properties for the numerical integration of ordinary differential equationsPhysics Reports, 536
A. Kosti, Z. Anastassi, T. Simos (2009)
An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problemsJournal of Mathematical Chemistry, 47
Stavros Stavroyiannis, T. Simos (2010)
A nonlinear explicit two-step fourth algebraic order method of order infinity for linear periodic initial value problemsComput. Phys. Commun., 181
MM Chawla, PS Rao (1986)
An Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems II Explicit MethodJ. Comput. Appl. Math., 15
TE Simos, G Psihoyios (2006)
Special issue: the international conference on computational methods in sciences and engineering 2004—prefaceJ. Comput. Appl. Math., 191
Z. Anastassi, T. Simos (2009)
A family of two-stage two-step methods for the numerical integration of the Schrödinger equation and related IVPs with oscillating solutionJournal of Mathematical Chemistry, 45
G. Quinlan, S. Tremaine (1990)
Symmetric Multistep Methods for the Numerical Integration of Planetary OrbitsThe Astronomical Journal, 100
S. Stavroyiannis, T. Simos (2009)
Optimization as a function of the phase-lag order of nonlinear explicit two-step P-stable method for linear periodic IVPsApplied Numerical Mathematics, 59
T. Simos (2008)
A family of four-step trigonometrically-fitted methods and its application to the schrödinger equationJournal of Mathematical Chemistry, 44
A. Cohen, M. Schmaltz, E. Katz, C. Rebbi, S. Glashow, R. Brower, S. Pi (2016)
Topics in Theoretical Physics
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Z. Anastassi, T. Simos (2005)
An optimized Runge-Kutta method for the solution of orbital problemsJournal of Computational and Applied Mathematics, 175
T. Monovasilis, Z. Kalogiratou, T. Simos (2011)
Two New Phase-Fitted Symplectic Partitioned Runge–Kutta MethodsInternational Journal of Modern Physics C, 22
I. Alolyan, T. Simos (2015)
Efficient low computational cost hybrid explicit four-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 53
T. Simos (2009)
Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problemsAppl. Math. Lett., 22
T. Simos (2000)
A new explicit Bessel and Neumann fitted eighth algebraic order method for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 27
T. Simos (2011)
Optimizing a class of linear multi-step methods for the approximate solution of the radial Schrödinger equation and related problems with respect to phase-lagCentral European Journal of Physics, 9
G. Avdelas, A. Konguetsof, T. Simos (2001)
A Generator and an Optimized Generator of High-Order Hybrid Explicit Methods for the Numerical Solution of the Schrödinger Equation. Part 2. Development of the Generator, Optimization of the Generator and Numerical ResultsJournal of Mathematical Chemistry, 29
Zhou Zhou, T. Simos (2016)
A new two stage symmetric two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the radial Schrödinger equationJournal of Mathematical Chemistry, 54
I. Alolyan, T. Simos (2015)
A high algebraic order multistage explicit four-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 53
Z. Anastassi, T. Simos (2012)
A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problemsJ. Comput. Appl. Math., 236
D. Sakas, T. Simos (2005)
A family of multiderivative methods for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 37
G. Papageorgiou, C. Tsitouras, I. Famelis (2001)
EXPLICIT NUMEROV TYPE METHODS FOR SECOND ORDER IVPs WITH OSCILLATING SOLUTIONSInternational Journal of Modern Physics C, 12
C. Tsitouras, I. Famelis, T. Simos (2017)
Phase-fitted Runge-Kutta pairs of orders 8(7)J. Comput. Appl. Math., 321
G. Panopoulos, Z. Anastassi, T. Simos (2011)
A NEW SYMMETRIC EIGHT-STEP PREDICTOR-CORRECTOR METHOD FOR THE NUMERICAL SOLUTION OF THE RADIAL SCHRÖDINGER EQUATION AND RELATED ORBITAL PROBLEMSInternational Journal of Modern Physics C, 22
Z. Kalogiratou, T. Monovasilis, T. Simos (2013)
A fourth order modified trigonometrically fitted symplectic Runge-Kutta-Nyström methodComput. Phys. Commun., 185
M. Chawla, P. Rao (1987)
An explicit sixth-order method with phase-lag of order eight for y ″= f ( t , y )Journal of Computational and Applied Mathematics, 17
(2015)
LaTeX Cookbook, pp
I. Alolyan, Z. Anastassi, T. Simos (2012)
A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problemsAppl. Math. Comput., 218
G. Panopoulos, Z. Anastassi, T. Simos (2013)
A NEW EIGHT-STEP SYMMETRIC EMBEDDED PREDICTOR-CORRECTOR METHOD (EPCM) FOR ORBITAL PROBLEMS AND RELATED IVPs WITH OSCILLATORY SOLUTIONSThe Astronomical Journal, 145
L. Ixaru, M. Rizea (1980)
A numerov-like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energiesComputer Physics Communications, 19
T. Simos (2004)
Dissipative trigonometrically-fitted methods for linear second-order IVPs with oscillating solutionAppl. Math. Lett., 17
D. Sakas, T. Simos (2005)
Multiderivative methods of eighth algebraic order with minimal phase-lag for the numerical solution of the radial Schrödinger equationJournal of Computational and Applied Mathematics, 175
A. Messiah (1961)
Quantum Mechanics
Minjian Liang, T. Simos (2016)
A new four stages symmetric two-step method with vanished phase-lag and its first derivative for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 54
G. Avdelas, A. Konguetsof, T. Simos (2001)
A Generator and an Optimized Generator of High-Order Hybrid Explicit Methods for the Numerical Solution of the Schrödinger Equation. Part 1. Development of the Basic MethodJournal of Mathematical Chemistry, 29
I. Alolyan, T. Simos (2016)
A family of two stages tenth algebraic order symmetric six-step methods with vanished phase-lag and its first derivatives for the numerical solution of the radial Schrödinger equation and related problemsJournal of Mathematical Chemistry, 54
G. Panopoulos, T. Simos, S. Arabia (2014)
A New Optimized Symmetric Embedded Predictor- Corrector Method (EPCM) for Initial-Value Problems with Oscillatory SolutionsApplied Mathematics & Information Sciences, 8
I. Alolyan, T. Simos (2016)
A new eight algebraic order embedded explicit six-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 54
T. Simos (2007)
Closed Newton-Cotes Trigonometrically-Fitted Formulae for Numerical Integration of the Schrödinger EquationComputing Letters, 3
Z. Kalogiratou, T. Simos (2003)
Newton--Cotes formulae for long-time integrationJournal of Computational and Applied Mathematics, 158
G. Panopoulos, T. Simos (2015)
An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknownJ. Comput. Appl. Math., 290
T. Simos (2008)
High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problemsComput. Phys. Commun., 178
T. Simos (2002)
Exponentially-fitted Runge-Kutta-Nystro"m method for the numerical solution of initial-value problems with oscillating solutionsAppl. Math. Lett., 15
Z. Kalogiratou, T. Monovasilis, T. Simos (2003)
Symplectic integrators for the numerical solution of the Schrödinger equationJournal of Computational and Applied Mathematics, 158
T. Monovasilis, Z. Kalogiratou, T. Simos (2008)
A family of trigonometrically fitted partitioned Runge-Kutta symplectic methodsAppl. Math. Comput., 209
A. Konguetsof, T. Simos (2003)
A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equationJournal of Computational and Applied Mathematics, 158
D. Berg, T. Simos, T. Simos (2017)
Three stages symmetric six-step method with eliminated phase-lag and its derivatives for the solution of the Schrödinger equationJournal of Mathematical Chemistry, 55
T. Simos (2014)
An explicit linear six-step method with vanished phase-lag and its first derivativeJournal of Mathematical Chemistry, 52
T. Simos (2008)
Closed Newton-Cotes Trigonometrically-Fitted Formulae for the Solution of the Schrodinger Equation
Z. Anastassi, T. Simos (2005)
Trigonometrically fitted Runge–Kutta methods for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 37
H. Vyver (2007)
An explicit Numerov-type method for second-order differential equations with oscillating solutionsComput. Math. Appl., 53
Z. Kalogiratou, T. Monovasilis, H. Ramos, T. Simos (2015)
A new approach on the construction of trigonometrically fitted two step hybrid methodsJ. Comput. Appl. Math., 303
G. Berghe, M. Daele (2010)
Exponentially fitted open Newton-Cotes differential methods as multilayer symplectic integrators.The Journal of chemical physics, 132 20
T. Simos (2008)
Closed Newton–Cotes trigonometrically-fitted formulae of high order for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 44
T. Simos (2010)
Exponentially and Trigonometrically Fitted Methods for the Solution of the Schrödinger EquationActa Applicandae Mathematicae, 110
T. Simos (2001)
A fourth algebraic order exponentially-fitted Runge-Kutta method for the numerical solution of the Schrödinger equationIma Journal of Numerical Analysis, 21
T. Simos (2014)
A new explicit four-step method with vanished phase-lag and its first and second derivativesJournal of Mathematical Chemistry, 53
D. Papadopoulos, T. Simos (2013)
The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström MethodAbstract and Applied Analysis, 2013
TE Simos, I Gutman (2005)
Papers presented on the international conference on computational methods in sciences and engineering (Castoria, Greece, September 12–16, 2003)MATCH Commun. Math. Comput. Chem., 53
K. Tselios, T. Simos (2003)
Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acousticsJournal of Computational and Applied Mathematics, 175
I. Alolyan, T. Simos (2011)
A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equationComput. Math. Appl., 62
I. Alolyan, T. Simos (2014)
A family of explicit linear six-step methods with vanished phase-lag and its first derivativeJournal of Mathematical Chemistry, 52
T. Simos, J. Vigo-Aguiar (2002)
Symmetric Eighth Algebraic Order Methods with Minimal Phase-Lag for the Numerical Solution of the Schrödinger EquationJournal of Mathematical Chemistry, 31
I. Alolyan, T. Simos (2014)
A Runge–Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 52
Zhongcheng Wang (2005)
P-stable linear symmetric multistep methods for periodic initial-value problemsComput. Phys. Commun., 171
G. Psihoyios, T. Simos (2005)
A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutionsJournal of Computational and Applied Mathematics, 175
T. Simos, J. Aguiar (2001)
A Modified Phase-Fitted Runge–Kutta Method for the Numerical Solution of the Schrödinger EquationJournal of Mathematical Chemistry, 30
T. Simos, T. Simos (2014)
A new explicit hybrid four-step method with vanished phase-lag and its derivativesJournal of Mathematical Chemistry, 52
I. Alolyan, T. Simos (2017)
New two stages high order symmetric six-step method with vanished phase–lag and its first, second and third derivatives for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 55
G. Panopoulos, Z. Anastassi, T. Simos (2008)
Two optimized symmetric eight-step implicit methods for initial-value problems with oscillating solutionsJournal of Mathematical Chemistry, 46
Yonglei Fang, Xinyuan Wu (2007)
A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problemsAppl. Math. Comput., 189
G. Psihoyios, T. Simos (2005)
Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equationJournal of Mathematical Chemistry, 37
Wei Zhang, T. Simos (2016)
A High-Order Two-Step Phase-Fitted Method for the Numerical Solution of the Schrödinger EquationMediterranean Journal of Mathematics, 13
G. Panopoulos, Z. Anastassi, T. Simos, T. Simos (2011)
A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutionsComput. Phys. Commun., 182
Kenan Mu, T. Simos (2015)
A Runge–Kutta type implicit high algebraic order two-step method with vanished phase-lag and its first, second, third and fourth derivatives for the numerical solution of coupled differential equations arising from the Schrödinger equationJournal of Mathematical Chemistry, 53
I. Alolyan, T. Simos (2014)
A hybrid type four-step method with vanished phase-lag and its first, second and third derivatives for each level for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 52
D. Papadopoulos, T. Simos (2013)
A Modified Runge-Kutta-Nystr¨ om Method by using Phase Lag Properties for the Numerical Solution of Orbital ProblemsApplied Mathematics & Information Sciences, 7
A. Kosti, Z. Anastassi, T. Simos (2011)
Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problemsComput. Math. Appl., 61
T. Simos (2003)
A Family of Trigonometrically-Fitted Symmetric Methods for the Efficient Solution of the Schrödinger Equation and Related ProblemsJournal of Mathematical Chemistry, 34
C. Tsitouras, I. Famelis, T. Simos (2011)
On modified Runge-Kutta trees and methodsComput. Math. Appl., 62
T. Monovasilis, Z. Kalogiratou, T. Simos (2003)
Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equationJournal of Mathematical Chemistry, 37
K. Tselios, T. Simos (2003)
Symplectic Methods for the Numerical Solution of the Radial Shrödinger EquationJournal of Mathematical Chemistry, 34
J. Lambert, I. Watson (1976)
Symmetric Multistip Methods for Periodic Initial Value ProblemsIma Journal of Applied Mathematics, 18
D. Papadopoulos, T. Simos (2011)
a New Methodology for the Construction of Optimized RUNGE-KUTTA-NYSTRÖM MethodsInternational Journal of Modern Physics C, 22
J. Dormand, Moawwad El-Mikkawy, P. Prince (1987)
Families of Runge-Kutta-Nystrom FormulaeIma Journal of Numerical Analysis, 7
T. Simos (2006)
A four-step exponentially fitted method for the numerical solution of the Schrödinger equationJournal of Mathematical Chemistry, 40
A. Raptis, A. Allison (1978)
Exponential-fitting methods for the numerical solution of the schrodinger equationComputer Physics Communications, 14
Z. Anastassi, T. Simos (2009)
Numerical multistep methods for the efficient solution of quantum mechanics and related problemsPhysics Reports
T. Simos, P. Williams (1997)
A finite-difference method for the numerical solution of the Schro¨dinger equationJournal of Computational and Applied Mathematics, 79
TE Simos (2015)
Multistage symmetric two-step P-stable method with vanished phase-lag and its first, second and third derivativesAppl. Comput. Math., 14
T. Simos (2013)
New open modified Newton Cotes type formulae as multilayer symplectic integratorsApplied Mathematical Modelling, 37
Z. Kalogiratou, T. Simos (2002)
Construction of Trigonometrically and Exponentially Fitted Runge–Kutta–Nyström Methods for the Numerical Solution of the Schrödinger Equation and Related Problems – a Method of 8th Algebraic OrderJournal of Mathematical Chemistry, 31
T. Monovasilis, Z. Kalogiratou, T. Simos (2012)
Exponentially fitted symplectic Runge-Kutta-Nyström methods, 1479
T. Simos (2010)
New closed Newton-Cotes type formulae as multilayer symplectic integrators.The Journal of chemical physics, 133 10
TE Simos (2003)
Closed Newton–Cotes trigonometrically-fitted formulae for long-time integrationInt. J. Mod. Phys. C, 14
H. Ramos, Z. Kalogiratou, T. Monovasilis, T. Simos (2015)
An optimized two-step hybrid block method for solving general second order initial-value problemsNumerical Algorithms, 72
T. Simos (2012)
New high order multiderivative explicit four-step methods with vanished phase-lag and its derivatives for the approximate solution of the Schrödinger equation. Part I: Construction and theoretical analysisJournal of Mathematical Chemistry, 51
M. Medvedev, T. Simos (2017)
Two stages six-step method with eliminated phase-lag and its first, second, third and fourth derivatives for the approximation of the Schrödinger equationJournal of Mathematical Chemistry, 55
I. Alolyan, T. Simos (2016)
A family of embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation: development and theoretical analysisJournal of Mathematical Chemistry, 54
M. Chawla, P. Rao (1986)
A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-valueJournal of Computational and Applied Mathematics, 15
Radojka Vujasin, Milan Senanski, Jelena Radi, M. Peria (2010)
A Comparison of Various Variational Approaches for Solving the One- dimensional Vibrational Schrödinger Equation
G. Panopoulos, T. Simos (2013)
An Optimized Symmetric 8-Step Semi-Embedded Predictor-Corrector Method for IVPs with Oscillating SolutionsApplied Mathematics & Information Sciences, 7
I. Alolyan, T. Simos (2013)
A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrödinger equationJournal of Mathematical Chemistry, 51
Z. Kalogiratou, T. Monovasilis, T. Simos (2010)
New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equationComput. Math. Appl., 60
T. Monovasilis, Z. Kalogiratou, T. Simos (2008)
Computation of the eigenvalues of the Schrödinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge Kutta methodsPhysics Letters A, 372
G. Psihoyios, T. Simos (2003)
Trigonometrically fitted predictor: corrector methods for IVPs with oscillating solutionsJournal of Computational and Applied Mathematics, 158
In this paper we develop an efficient six-step method for the solution of the Schrödinger equation and related problems. The characteristics of the new obtained scheme are: It is of twelfth algebraic order. It has three stages. It has vanished phase-lag. It has vanished its derivatives up to order two. All the stages of the scheme are approximations on the point $$x_{n+3}$$ x n + 3 . This method is developed for the first time in the literature. A detailed theoretical analysis of the method is also presented. In the theoretical analysis, a comparison with the the classical scheme of the family (i.e. scheme with constant coefficients) and with recently developed algorithm of the family with eliminated phase-lag and its first derivative is also given. Finally, we study the accuracy and computational effectiveness of the new developed algorithm for the on the approximation of the solution of the Schrödinger equation. The above analysis which is described in this paper, leads to the conclusion that the new algorithm is more efficient than other known or recently obtained schemes of the literature.
Journal of Mathematical Chemistry – Springer Journals
Published: Mar 22, 2017
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