NEW CONSTRUCTION OF HIGHER-ORDER LOCAL CONTINUOUS PLATFORMS FOR ERROR CORRECTION METHODS

Abstract

Error correction method (ECM) [6,1 which has been recently developed, is based on the construction of a local approximation to the solution on each time step, and has the excellent convergence order 0(h(2p+2)), provided the local approximation has a local residual error 0(h(p)). In this paper, we construct a higher-order continuous local platform to develop higher-order semi-explicit one-step ECM for solving initial value time dependent differential equations. It is shown that special choices of parameters for the local platform can lead to the improvement of the well-known explicit fourth and fifth order Runge-Kutta methods. Numerical experiments demonstrate the theoretical results.