Numerical Solution of Integral Algebraic Equations with Singular Points Using the Least Squares Method

We conduct a numerical study of integral algebraic equations (IAEs) with singular points, which pose significant challenges for standard computational methods. The presence of singular points often renders classical discretization schemes unstable and inaccurate. This work explores the reformulation of such problems using a least squares framework to restore numerical stability. By recasting the singular IAE as a minimization problem, the least squares method effectively handles the non-integrability and ill-conditioning inherent in direct approaches. We provide a numerical analysis of the proposed scheme and present results from several test cases, demonstrating its superior performance in terms of the convergence rate and solution quality compared to conventional methods. Our findings establish the least squares method as a viable and effective tool for solving singular IAEs.