A high accuracy compact semi-constant mesh off-step discretization in exponential form for the solution of non-linear elliptic boundary value problems

Abstract

This paper describes a novel implicit method of order 2 in y- and 3 in x-direction in exponential form, by exploiting off-step discretization to solve numerically non-linear elliptic partial differential equations in a rectangular region. We use variable mesh in x-direction and constant mesh in y-direction in order to solve convection–diffusion equation for large values of the coefficient of convection term. This method uses 9-point compact stencil. Detailed derivation and convergence procedure of the proposed method have been discussed. The method has been generalized to solve non-linear elliptic equations in vector form. The method is validated on several benchmark problems showing that formulation produces satisfactory results.