Variation of parameters method with an auxiliary parameter for initial value problems

Abstract

In this paper, an unknown auxiliary parameter is inserted in Variation of Parameter Method to solve Evolution and RLW equations. The proposed algorithm is very effective and is practically well suited for use in these problems. Three practical examples are given to verify the accuracy and efficiency of the developed technique. Comparison with the standard VPM is made to show the reliability and efficiency of the proposed algorithm. Keywords: Variation of Parameter Method (VPM), Auxiliary parameter, Evolution and RLW equations