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A numerical method for solving fourth-order integro-differential equations is presented. Thismethod is based on replacement of the unknown function by a truncated series of well-knownshifted Chebyshev expansion of functions. An approximate formula of the integer derivative isintroduced. The introduced method converts the proposed equation by means of collocationpoints to system of algebraic equations with shifted Chebyshev coefficients. Thus, by solvingthis system of equations, the shifted Chebyshev coefficients are obtained. Special attention isgiven to study the convergence analysis and derive an upper bound of the error of the presentedapproximate formula. Numerical results are performed in order to illustrate the usefulness andshow the efficiency and the accuracy of the present work.

Numerical and Analytical Study for Fourth-Order Integro-Differential Equations Using a Pseudospectral Method