Application of the Second Kind Chebyshev Galerkin Method for Solving a Weakly Singular Fredholm Integro-Differential Equation
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In this paper, we present a comprehensive numerical approach to solve nonlinear Fredholm integro-differential equations with weakly singular kernels. Our method combines the power of Chebyshev polynomials of the second kind, the operational matrix of integration, and the Galerkin method. By applying the Picard successive approximations technique, we effectively address the resulting nonlinear algebraic system, thereby obtaining the desired numerical solution for the given equation. To validate the efficacy of our proposed approach, we provide several numerical experiments which demonstrate the accuracy and reliability of our process.
Abstract
In this paper, we present a comprehensive numerical approach to solve nonlinear Fredholm integro-differential equations with weakly singular kernels. Our method combines the power of Chebyshev polynomials of the second kind, the operational matrix of integration, and the Galerkin method. By applying the Picard successive approximations technique, we effectively address the resulting nonlinear algebraic system, thereby obtaining the desired numerical solution for the given equation. To validate the efficacy of our proposed approach, we provide several numerical experiments which demonstrate the accuracy and reliability of our process.