Solving generalized Abel's integral equations of the first and second kinds via Taylor-collocation method
Provides a numerical solution method for a class of integral equations, but the improvement over existing methods is not quantified.
The authors developed a Taylor-collocation method to numerically solve generalized Abel's integral equations of the first and second kinds, demonstrating accuracy and efficiency through several examples with error analysis.
The aim of this paper is to present an efficient numerical procedure to approximate the generalized Abel's integral equations of the first and second kinds. For this reason, the Taylor polynomials and the collocation method are applied. Also, the error analysis of presented method is illustrated. Several examples are approximated and the numerical results show the accuracy and efficiency of this method.