Parallel Solver for Oscillatory Stiff Systems of ODEs

Abstract

The aim of this study will be to design Parallel solver (PS) for oscillatory stiff systems of ordinary differential equations (ODEs). PS will be constructed via a type of specially transformed exponentially fitted multinomial approximant in accordance with the behaviour of the solution. The method of interpolation and collocation will be utilized. The principal local truncation errors of PS will be used to derive a suitable step size and decide the error tolerance criteria for establishing the convergence of PS. Some examples of stiff ODEs will be examined and compared with existing methods to show case the efficiency and accuracy of the scheme. Parallel solver will be seen as a unique model for solving stiff ODEs without dependent on absolute stability as required by backward differentiation formula.