A Novel Numerical Algorithm of Numerov Type for 2D Quasi-linear Elliptic Boundary Value Problems

Abstract

In this article, using three function evaluations, we discuss a nine-point compact scheme of O(Δ y² + Δ x⁴) based on Numerov-type discretization for the solution of 2D quasi-linear elliptic equations with given Dirichlet boundary conditions, where Δy > 0 and Δx > 0 are grid sizes in y- and x-directions, respectively. Iterative methods for diffusion-convection equation are discussed in detail. We use block iterative methods to solve the system of algebraic linear and nonlinear difference equations. Comparative results of some physical problems are given to illustrate the usefulness of the proposed method.

Keywords:

• Quasi-linear elliptic equations
• Numerov-type algorithm
• Diffusion-convection equation
• Nonlinear convection equation
• Poisson's equation in polar coordinates
• Block-iterative methods

ACKNOWLEDGEMENT

The authors thank the reviewers for their valuable suggestions, which substantially improved the standard of the paper.