Analysis demonstrates theoretical accuracy and convergence of the spectral collocation method for GAIEs, indicating its effectiveness in numerical solutions.
This paper is devoted to the spectral collocation method using Jacobi polynomials for Generalized Abel’s integral equations (GAIEs). Jacobi polynomials are used to approximate the solution which reduces GAIEs to a system of algebraic equations. To show the theoretical accuracy of the proposed method, convergence analysis has been proved. Also, the error estimate is approximated which shows that the approximation will converge to the exact solution. Two numerical examples are considered to verify and validate the theoretical results. Further, numerical results are compared using some particular cases of Jacobi polynomials.
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Sharma et al. (2025) studied this question.
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