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In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integro-differential equations (FVHIDEs) under mixed condition. This method of estimating the solution, transforms the nonlinear (FVHIDEs) to matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system of nonlinear algebraic equations with the unknown Bessel coefficients. Present results and comparisons demonstrate that our estimate has good degree of accuracy and this method is more valid and useful than other methods.

Keywords: Bessel polynomials, Integro-differential equations, Collocation, Fredholm, Volterra, Hammerestein

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