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Home  >  Volume 48

4. NEW MULTIPLE INTEGRAL COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS by A.O. Adewumi, O.M. Ogunlaran and A.F. Adebisi. Volume 48 (Sept. & Nov., 2018 Issue), pp29 –34
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NEW MULTIPLE INTEGRAL COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

A.O.  Adewumi, O.M. Ogunlaran and A.F. Adebisi.

Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Osun State, Nigeria.

Department of Mathematics and Statistics, Bowen University, Iwo, Osun State, Nigeria.

Department of Mathematical and Physical Sciences, Osun State University, Osogbo, Osun State, Nigeria.

Abstract

This paper presents new collocation approaches for the numerical solutions of linear and nonlinear foruth-order Volterra integro-differential equations. These approaches involve the use of Chebyshev and Berstein polynomials as basis functions. Approximations to the lower order derivatives of the function through successive integration of Chebyshev and Berstein polynomials to the highest order derivatives are generated. We successfully implemented the new approaches on both linear and nonlinear integro-differential equations. Numerical results show that the new methods are accurate and highly promising in comparison with other numerical methods.

Keywords: Volterra integro-differential equations, Collocation, Chebyshev polynomials, Berstein polynomials, Multiplr integral.

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