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<p>This study delves into an innovative approach that combines projection methods utilizing Jacobi polynomials and Lavrentiev regularization techniques, aiming to solve the first kind Abel equation. The proposed numerical method proficiently converts the solution of this first kind, ill–posed weakly singular integral equation into a solution of a well–posed linear system of algebraic equations. The proposed technique is subjected to a comprehensive theoretical analysis, followed by a series of rigorous numerical tests aimed at showcasing the validity and efficiency of our approach.</p>

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A regularized Jacobi scheme for first kind Abel integral equation

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Tahar Bechouat,
  • Nadjib Boussetila

摘要

This study delves into an innovative approach that combines projection methods utilizing Jacobi polynomials and Lavrentiev regularization techniques, aiming to solve the first kind Abel equation. The proposed numerical method proficiently converts the solution of this first kind, ill–posed weakly singular integral equation into a solution of a well–posed linear system of algebraic equations. The proposed technique is subjected to a comprehensive theoretical analysis, followed by a series of rigorous numerical tests aimed at showcasing the validity and efficiency of our approach.