Numerical Solution for Couple Elliptic Boundary Value Problem

The Galerkin finite elements method (GAFEM) is used to find the numerical solution (NS) of the couple linear elliptic boundary value problem (CLEBVP). The solution of the CLEBVP is approximated by a linear combination of piecewise linear and continuous basis functions, upon substituting this approximated solution into the CLEBVP the problem then reduces to solve a “Galerkin” linear algebraic system (GALAS). This system is solved by using the classical Cholesky method (CChM). Some illustrative examples are given; to show the high efficiency of the GAFEM to solve such for the CLEBVPs. Figures provide the NS with “results”.