NUMERICAL SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER WITH INITIAL CONDITIONS USING COLLOCATION APPROACH

Document Type : Regular research papers

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1 Department of Mathematics and Statistics, Federal University Wukari, Taraba State

2 Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria.

3 Department of Mathematics, University of Ilesa, Ilesa, Osun State, Nigeria

4 Federal College of Dental Technology and Therapy, Enugu, Nigeria

Abstract

In this paper, we develop and implement a numerical method for the solution of Volterra integro- differential equations of fractional order using the collocation method. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the polynomial collocation method. We then solve the algebraic equation using matrix inversion. The analysis of the developed method was investigated, and the solution was found to be continuous, and convergent. The uniqueness of the solution was also proven. Numerical examples were considered to test the consistency and efficiency of the method.
In this paper, we develop and implement a numerical method for the solution of Volterra integro- differential equations of fractional order using the collocation method. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the polynomial collocation method. We then solve the algebraic equation using matrix inversion. The analysis of the developed method was investigated, and the solution was found to be continuous, and convergent. The uniqueness of the solution was also proven. Numerical examples were considered to test the consistency and efficiency of the method.

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