A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations

A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential... Differ Equ Dyn Syst https://doi.org/10.1007/s12591-018-0427-5 ORIGINAL RESEARCH A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations 1 2 3 R. K. Mohanty · Sachin Sharma · Swarn Singh © Foundation for Scientific Research and Technological Innovation 2018 Abstract In this article, we proposed a new two-level implicit method of accuracy two in time and four in space based on spline in compression approximations using two half-step points and a central point on a uniform mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differential equations subject to appropriate initial and natural boundary conditions prescribed. The proposed method is derived directly from the continuity condition of the first order derivative of the non-polynomial compression spline function. The stability analysis for a model problem is discussed. The method is directly applicable to problems in polar systems. To demonstrate the strength and utility of the proposed method, we have solved generalized Burgers–Huxley equation, generalized Burgers–Fisher equation, coupled Burgers-equations and parabolic equations with singular coefficients. We show that the proposed method enables us to obtain high accurate solution for high Reynolds number. Keywords Quasi-linear parabolic equations · Spline http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations and Dynamical Systems Springer Journals

A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations

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Publisher
Springer India
Copyright
Copyright © 2018 by Foundation for Scientific Research and Technological Innovation
Subject
Mathematics; Mathematics, general; Engineering, general; Computer Science, general
ISSN
0971-3514
eISSN
0974-6870
D.O.I.
10.1007/s12591-018-0427-5
Publisher site
See Article on Publisher Site

Abstract

Differ Equ Dyn Syst https://doi.org/10.1007/s12591-018-0427-5 ORIGINAL RESEARCH A New Two-Level Implicit Scheme for the System of 1D Quasi-Linear Parabolic Partial Differential Equations Using Spline in Compression Approximations 1 2 3 R. K. Mohanty · Sachin Sharma · Swarn Singh © Foundation for Scientific Research and Technological Innovation 2018 Abstract In this article, we proposed a new two-level implicit method of accuracy two in time and four in space based on spline in compression approximations using two half-step points and a central point on a uniform mesh for the numerical solution of the system of 1D quasi-linear parabolic partial differential equations subject to appropriate initial and natural boundary conditions prescribed. The proposed method is derived directly from the continuity condition of the first order derivative of the non-polynomial compression spline function. The stability analysis for a model problem is discussed. The method is directly applicable to problems in polar systems. To demonstrate the strength and utility of the proposed method, we have solved generalized Burgers–Huxley equation, generalized Burgers–Fisher equation, coupled Burgers-equations and parabolic equations with singular coefficients. We show that the proposed method enables us to obtain high accurate solution for high Reynolds number. Keywords Quasi-linear parabolic equations · Spline

Journal

Differential Equations and Dynamical SystemsSpringer Journals

Published: May 31, 2018

References

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