A high accuracy compact semi-constant mesh off-step discretization in exponential form for the solution of non-linear elliptic boundary value problems. Issue 4 (3rd April 2021)

• Record Type: Journal Article
• Authors: Manchanda, Geetan; Mohanty, R. K.; Khan, Arshad
• Is Part Of: Journal of difference equations and applications. Volume 27:Issue 4(2021)
• Page Start: 531
• Page End: 556
• Publication Date: 2021-04-03
• Subjects: Non-linear elliptic equations -- off-step exponential approximation -- convergence analysis -- Burger's equation -- convection–diffusion equation -- Poisson equation in r–z plane -- Navier–Stokes equations of motion; 65N06 -- 65N12; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2021.1920936
• Languages: English
• ISSNs: 1023-6198

Abstract

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 2 D 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.