A Family of Variable Step-Size Meshes Fourth-Order Compact Numerical Scheme for (2+1)-Dimensions Burger’s-Huxley, Burger’s-Fisher and Convection-Diffusion Equations
Year: 2022
Author: Navnit Jha, Madhav Wagley
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 2 : pp. 245–276
Abstract
Existing numerical schemes, maybe high-order accurate, are obtained on uniformly spaced meshes and challenges to achieve high accuracy in the presence of singular perturbation parameter, and nonlinearity remains left on nonuniformly spaced meshes. A new scheme is proposed for nonlinear 2D parabolic partial differential equations (PDEs) that attain fourth-order accuracy in $xy$-space and second-order exact in the temporal direction for uniform and nonuniform mesh step-size. The method proclaims a compact character using nine-point single-cell finite-difference discretization on a nonuniformly spaced spatial mesh point. A description of splitting compact operator form to the convection-dominated equation is obtained for implementing alternating direction implicit scheme. The procedure is examined for consistency and stability. The scheme is applied to linear and nonlinear 2D parabolic equations: convection-diffusion equations, Burger’s-Huxley, Burger’s-Fisher and coupled Burger’s equation. The technique yields the tridiagonal matrix and computed by the Thomas algorithm. Numerical simulations with linear and nonlinear problems corroborate the theoretical outcome.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.245
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 2 : pp. 245–276
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Nonlinear parabolic partial differential equations (PDEs) Two-Dimensions Burger’s-Huxley equation Boussinesq equation Convection-Diffusion equation Compact-Scheme Stability Errors and numerical order.