Osman Rasit Isik1and Tarkan ¨Oner2

Abstract

In this study, we introduce two algorithms to numerically solve any initial value problem (IVP). These algorithms dependon time relaxation model (TRM) which is obtained adding a time relaxation term into IVP. Discretizing TRM by using backward Euler(BE) method gives the first algorithm. Similarly, the second algorithm is followed by using trapezoid (TR) time stepping scheme . Undersome conditions, the first algorithm increases the order of convergence from one to two and the second one increases the order fromtwo to three. Thus, more accurate results can be obtained. To verify the accuracy of the methods, they are applied to some numericalexamples. Numerical results overlap with the theoretical results