The purpose of this paper is to present a method for approximate solution of initial value problems of ordinary differential equation by the double exponential transformation. The original problem is transformed into a Volterra integral equation and it is solved via the indeﬁnite integration formula derived by Muhammad and Mori. A remarkable advantage of the double exponential transformation technique for solving initial value problems in this method is that it is easily implemented and gives a result with high accuracy also for problems with end point singularities and for stiﬀ problems. The high accuracy of the method proposed in this paper is conﬁrmed by numerical examples and an exponential convergence rate exp(−_cN_/ log N) is attained in almost all cases.
Cite this article
Ahniyaz Nurmuhammad, Mayinur Muhammad, Masatake Mori, Numerical Solution of Initial Value Problems Based on the Double Exponential Transformation. Publ. Res. Inst. Math. Sci. 41 (2005), no. 4, pp. 937–948DOI 10.2977/PRIMS/1145474601