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

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, University of Lagos, Lagos, Nigeria

2 Department of Mathematics, Caleb University, Imota, Lagos, Nigeria

3 Department of Mathematics, Covenant University, Canaan Land, Ota, Ogun State, Nigeria

4 Department of Mathematics, Nigerian Army University, Biu, Borno State, Nigeria

Abstract

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

Keywords

Main Subjects

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### History

• Receive Date: 15 November 2022
• Revise Date: 31 March 2023
• Accept Date: 02 April 2023