@Article{JNMA-4-2,
author = {Navnit, Jha and Wagley, Madhav},
title = {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},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2022},
volume = {4},
number = {2},
pages = {245--276},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2022.245},
url = {https://global-sci.com/article/87921/a-family-of-variable-step-size-meshes-fourth-order-compact-numerical-scheme-for-21-dimensions-burgers-huxley-burgers-fisher-and-convection-diffusion-equations}
}