Efficient Numerical Approximation Methods for Solving High-Order Integro-Differential Equations

Abstract

In this work, we developed an approximate solution of high-order integro-differential equations (IDEs.) via the third kind of Chebyshev and Hermite Polynomials as basis functions using standard collocation method for Volterra and Fredholm integro-differential equations (IDEs). An assumed approximate solution is substituted into the given problem considered. After simplifications, the like terms of the unknown constants to be determined were collected and collocate at point ?=??, where ?? are the zeros of the Chebyshev and Hermite polynomials. The resulting equations are then put into matrix form which is then solved via Maple 18 software to obtain the unknown constants ??(?≥0). These are substituted back to obtain our approximate solution. Comparison is made with the two basis functions aforementioned in terms of errors obtained. Given numerical examples shows that the methods are efficient, reliable and less computational for the numerical solution of the integro-differential equation.