TY - JOUR
T1 - 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
AU - Jha , Navnit
AU - Wagley , Madhav
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 245
EP - 276
PY - 2022
DA - 2022/06
SN - 4
DO - http://doi.org/10.12150/jnma.2022.245
UR - https://global-sci.org/intro/article_detail/jnma/20706.html
KW - Nonlinear parabolic partial differential equations (PDEs), Two-Dimensions Burger’s-Huxley equation, Boussinesq equation, Convection-Diffusion equation, Compact-Scheme, Stability, Errors and numerical order.
AB - <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>