Fourth‐order difference method for quasilinear Poisson equation in cylindrical symmetry

Abstract

SUMMARYWe propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method.

High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region

“…In practical, numerical approximations for nonlinear EPDEs are of extreme interest in applied physics and applied mathematics. Different approximations have been developed for solving EPDEs, in particular finite element methods (FEMs), finite volume methods (FVMs) and FDMs [17] , [18] , [19] , [20] , [21] , [22] . Ananthakrishnaiah et al [23] have analyzed a fourth order approximation for 2D mildly nonlinear EPDEs.…”

Higher order approximation in exponential form based on half-step grid-points for 2D quasilinear elliptic BVPs on a variant domain

“…Some related research works done in the past by various authors are as follows: FDMs of different orders of approximation for solving linear and non-linear BVPEs have been developed by Jain et al. [ 7 , 8 , 10 ] and Mohanty [ 9 , 15 , 24 ]. In the year 1995, an FDM of order four for a two-dimensional (2D) mildly non-linear BVPE has been developed by Saldanha and Ananthakrishnaiah et al.…”

A compact high resolution semi-variable mesh exponential finite difference method for non-linear boundary value problems of elliptic nature

“…The integral of the partial differential equations (PDEs) and associated boundary and initial assumptions are an essential part in modeling various phenomena in the fields of sciences (fluid dynamics, heat flow etc) as well as economics [1,3,16,20,21]. But very few PDEs possess an analytical solution.…”