Numerical Solution of Volterra-Fredholm-Hammerstein Integral Equations by the Tau Method with the Bernstein Multi-scaling Functions
نویسندگان
چکیده
Abstract: In this work, the operational Tau method is presented to find the solutions of the linear and nonlinear Volterra-Fredholm-Hammerstein integral equations (VFHIEs) of the second kind. Some simple matrices in extension of Tau method for the numerical solutions of VFHIEs is applied. In fact, operational Tau method converts the integral parts of the desired VFHIEs to some operational matrices and constructs the algebraic equivalent representation of the problems. This representation is a system whose solution gives the components of the vector solution. Bernstein multi-scaling functions are applied as the basic polynomial. Finally some examples are given to show the high accuracy of the method with Bernstein multi-scaling functions basic.
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