Approximate Solution of the Second Order Initial Value Problem by Using Epsilon Modified Block-Pulse Function

Subject Areas : International Journal of Mathematical Modelling & Computations

Mahnaz Mohammadi ¹ , Alireza Vahidi ² , Saeid Khezerloo ³

1 - Department of Mathematics, Islamic Azad University-south Tehran Branch, Tehran, Iran.
2 - Department of mathematics, Islamic Azad University-shahr rey Branch, Tehran, Iran
3 - Department of Mathematics, Islamic Azad university--south Tehran Branch, Tehran, Iran.

Received: 2019-06-10 Accepted : 2019-09-15 Published : 2019-12-25

Keywords: Volterra integral equation, Initial value problems, Runge–Kutta method, εmodified block–pulse function,

Abstract :

The present work approaches the problem of achieving the approximate solution of the second order initial value problems (IVPs) via its conversion into a Volterra integral equation of the second kind (VIE2). Therefore, we initially solve the IVPs using Runge–Kutta of the forth–order method (RK), and then convert it into VIE2, and apply the εmodified block–pulse functions (εMBPFs) and their operational matrix for solving VIE2, which can be transformed to a lower triangular system of algebric equations. Numerical examples show that the proposed scheme has a suitable degree of accuracy.