TWO-STEP INTEGRAL COLLOCATION-VARIATIONAL ITERATION METHOD FOR THE SOLUTIONS OF INTEGRO-DIFFERENTIAL

An algorithm for solving integro-differential equations based on integral collocation and variational iteration is provided in this study. Integro-differential equations are first reduced to a system of integral equations, and then all of the derivatives in the new system of integral equations are substituted with their equivalent new derivatives. The equations for lower-order derivatives and the function itself were generated by approximating the nth order derivative with truncated Chebyshev series and then integrating n-times. The residual equation, which is collocated at the chosen collocation sites, is created after the second iteration, and extra n equations are also obtained from the boundary conditions. Computational results for test instances are provided to demonstrate the novel method's effectiveness, dependability, application, and efficiency. It is demonstrated that the method's solutions have a very high degree of accuracy..

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