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
Differential Equations and Dynamical Systems – Springer Journals
Published: May 31, 2018
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