TITLE:
Block Unification Scheme for Elliptic, Telegraph, and Sine-Gordon Partial Differential Equations
AUTHORS:
Samuel Jator
KEYWORDS:
Extended Block Method, Elliptic and Hyperbolic PDEs, Method of Lines
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.5 No.2,
June
23,
2015
ABSTRACT: In this paper, we use the method of lines to convert elliptic and hyperbolic partial differential equations (PDEs) into systems of boundary value problems and initial value problems in ordinary differential equations (ODEs) by replacing the appropriate derivatives with central difference methods. The resulting system of ODEs is then solved using an extended block Numerov-type method (EBNUM) via a block unification technique. The accuracy and speed advantages of the EBNUM over the finite difference method (FDM) are established numerically.