Compact half step approximation in exponential form for the system of 2D second-order quasi-linear elliptic partial differential equations

Abstract

ABSTRACTThis paper deals with devising a novel exponential scheme, implicit in nature, using half step discretization of order four for computing the numerical solution of quasi-linear elliptic partial differential equations of the type , . Nine mesh points in a single compact cell are being used in this method. An elaborate convergence analysis of the proposed method has been worked out. The technique for a scalar equation is eventually extended to solve the systems of quasi-linear elliptic equations. The technique is then applied to noteworthy problems and computational outcomes corroborate the theoretical rate of convergence. Linear and non-linear singular problems are tackled separately ensuring the usage of nine spatial grid points of a single computing cell.