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Series solution to the high-order integro-differential equations. (English) Zbl 1199.65420
Summary: The problem of solving high-order integro-differential equtions has special importance in engineering and science and constitutes a good model for many systems in various fields. In this paper, series solutions of the problem under consideration are presented by means of the homotopy analysis method. The numerical examples show the rapid convergence of the series constructed by this method to the exact solution. Moreover, this technique does not require any discretization, linearization or small perturbations and therefore significantly reduces numerical computations.
MSC:
65R20Integral equations (numerical methods)
65H20Global numerical methods for nonlinear algebraic equations, including homotopy approaches
45J05Integro-ordinary differential equations
45G10Nonsingular nonlinear integral equations