New multiple integral collocation methods for the numerical solution of fourth-order integro-differential equations

Abstract

This paper presents new collocations approaches for the numerical solutions of linear and non-linear fourth-order Volterra integro-differential equations. These approaches involves 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 non-linear integro-differential equations. Numerical results show that the new methods are accurate and highly promising in comparison with other numerical methods.