Criterion for the stability of numerical integration methods for the solution of systems of differential equations

The prob le m of studyin g the growth of th e error is most importa nt for th e num e ri cal so luti on of. differential eq uations. In thi s paper th e Wilrs crite rion is gene raJized to be a ppli ed for sys tems of diffe re ntial eq uations. A ge neral th eo re m is inves tigated and regions of stability have to be determined. The use of an electroni c co mputer is more esse ntial for s uc h region s to be c haracterized. These regions of stability have th e property that , th e e rror introdu ced at any stage te nd s to decay. The region s of stabi lity for partic ular numeri cal methods are exp li citl y determin ed.