A fractional splitting algorithm for non-overlapping domain decomposition

In this paper we study the convergence of the non overlapping domain decomposition for solving large linear system arising from semi discretization of two dimensional initial value problem with homogeneous boundary conditions, and solved by implicit time stepping using first and, two alternatives of second order FS-methods. The interface values along the artificial boundary condition line axe found using explicit forward Euler's method for the first order FS-method, and for the second order FS-method to use extrapolation procedure for each spatial variable individually. The solution by the non overlapping domain decomposition with FS-method is applicable to problems that requires the solution on non uniform meshes for each spatial variables which will unable us to use different time stepping over different subdomains, and with the possibility of extension to three dimensional problem.