Fourth‐order difference methods for the system of 2D nonlinear elliptic partial differential equations

Abstract

We present the fourth-order finite difference methods for the system of 2D nonlinear elliptic equations using 9-grid points on a square region R subject to Dirichlet boundary conditions. The method has been tested on viscous, incompressible 2D Navier-Stokes equations. The numerical results show that the proposed methods produce accurate and oscillation-free solutions for large Reynolds numbers.

A new compact high order off-step discretization for the system of 2D quasi-linear elliptic partial differential equations

“…Author details 1 Department of Applied Mathematics, Faculty of Mathematics and Computer Science, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India.…”

Numerical Study of Liquid Metal MHD Flow through a Square Duct under the Action of Strong Transverse Magnetic Field

“…In view of complexities in seeking closed form solutions, numerical solutions are considered. These equations are expressed in finite difference scheme followed by Schmidit [15]. The mesh system considered involves grid points with uniform spacing of Δx=0.0625 and Δy=0.025.…”

Fourth-order compact finite difference methods and monotone iterative algorithms for semilinear elliptic boundary value problems

“…The main idea of these methods is to increase the accuracy of the standard central finite difference approximation from the second-order to the fourth-order by approximating compactly the leading truncation error terms. In a similar manner, a class of fourth-order compact finite difference methods were proposed in [20][21][22] for some second-order and fourth-order semilinear elliptic differential equations. In all these works (except [22]), the main concern is the construction of the method.…”