A NUMERICAL METHOD FOR SOLVING THE INITIAL VALUE PROBLEMS OF STIFF ORDINARY DIFFERENTIAL EQUATIONS

This paper presents a numerical method for the solution of a stiff system of ordinary differential equations. The basic idea is to multiply both sides of a stiff system by a sufficiently small number ε, then construct an equivalent linear system with constant coefficients. At the grid points, combine the two systems and find the values of the right hand side of the linear system, then set up schemes for numerical integration.The schemes arc characterized by implicit-unconditional stability and explicit-ahnost-unconditional stability. For the implicit scheme, a convergent iteration process is given. The schemes are also applicable to systems of ordinary differential equations with right hand side functions having the denominators equal to zero at some points.This method has been further extended to the following:1. For the m-dhnensional heat conduction problem, an explicit-unconditionally stable scheme has been given.2. For a system of linear algebraic equations with the coefficient matrix symmetric pos