A highly accurate trivariate spectral collocation method of solution for two-dimensional nonlinear initial-boundary value problems

F.M. Samuel and S.S. Motsa

Applied Mathematics and Computation, 2019, vol. 360, issue C, 221-235

Abstract: In this paper, we propose a new numerical method namely, the trivariate spectral collocation method for solving two-dimensional nonlinear partial differential equations (PDEs) arising from unsteady processes. The problems considered are nonlinear PDEs defined on regular geometries. In the current solution approach, the quasi-linearization method is used to simplify the nonlinear PDEs. The solutions of the linearized PDEs are assumed to be trivariate Lagrange interpolating polynomials constructed using Chebyshev Gauss-Lobatto (CGL) points. A purely spectral collocation-based discretization is employed on the two space variables and the time variable to yield a system of linear algebraic equations that are solved by iteration. The numerical scheme is tested on four typical examples of nonlinear PDEs reported in the literature as a single equation or system of equations. Numerical results confirm that the proposed solution approach is highly accurate and computationally efficient when applied to solve two-dimensional initial-boundary value problems defined on small time intervals and hence it is a reliable alternative numerical method for solving this class of problems. The new error bound theorems and proofs on trivariate polynomial interpolation that we present support findings from the numerical simulations.

Keywords: Trivariate lagrange interpolating polynomials; Spectral collocation; Two-dimensional PDEs; Time dependent; CGL points (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:360:y:2019:i:c:p:221-235

DOI: 10.1016/j.amc.2019.04.082

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