Stable high order implicit methods for the numerical solution of systems of differential equations

Abstract

Some stable high order implicit methods for the solution of a system of differential equations of the form [equation: see PDF] where M is a constant banded matrix or of special form, are given. They require the solution at each step of more than one set of simultaneous linear equations but the coefficient matrix is the same for each set. Applications to the numerical solution of the heat conduction equation are given.