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

International Journal of Mathematical Modelling & Computations

مقاله 4، دوره 9، 4 (Fall) - شماره پیاپی 36، اسفند 2019، صفحه 283-295   

نوع مقاله: Review Article

نویسندگان

Mahnaz Mohammadi^{* 1}؛ Alireza Vahidi²؛ Saeid Khezerloo³

¹Department of Mathematics, Islamic Azad University-south Tehran Branch, Tehran, Iran.

²Department of mathematics, Islamic Azad University-shahr rey Branch, Tehran, Iran

³Department of Mathematics, Islamic Azad university--south Tehran Branch, Tehran, Iran.

چکیده

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.

کلیدواژه‌ها

Initial value problems؛ Runge–Kutta method؛ Volterra integral equation؛ εmodified block–pulse function