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Spectral Collocation Method for Generalized Abel’s Integral Equations

Author

Listed:
  • Shiva Sharma

    (Assistant Professor, Department of Mathematics, K P College Murliganj, Madhepura Bihar-852122, India.)

  • Saroj Kumar

    (Research Scholar, Department of Mathematics, B N Mandal University, Madhepura Bihar-852113, India)

Abstract

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.

Suggested Citation

  • Shiva Sharma & Saroj Kumar, 2025. "Spectral Collocation Method for Generalized Abel’s Integral Equations," International Journal of Latest Technology in Engineering, Management & Applied Science, RSIS International, vol. 14(8), pages 1418-1427, August.
    • Handle: RePEc:bjf:ijltem:v:14:y:2025:i:8:a:1754
    DOI: 10.51583/IJLTEMAS.2025.1408000181
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