Polynomial collocation method for initial value problem of mixed integro-differential equations

Abstract

This paper presents the development and implementation of a numerical method forthe solution of one dimensional Mixed Fredholm Volterra Intergro-Differential Equations(MFVIDEs). The new technique transformed MFVIDEs into an integral equation whichis then approximated using a polynomial collocation method. Standard collocation pointsare then used to convert the problem into a system of algebraic equations. Some numericalexamples are used to test the efficiency and accuracy of the method. The results showthat the new method is efficient, accurate and easy to implement.

Keywords

• one dimensional fredholm-volterra equations
• integro-differential equations
• polynomial collocation
• standard collocation points
• integral equations