ABSTRACT
A novel numerical algorithm using triangular orthogonal functions is developed to solve Abel’s integral equation of the first and second kind. The convergence analysis is carried out theoretically and numerically to prove that the proposed numerical algorithm can offer accurate approximate solutions that are very close to the true solutions of Abel’s integral equations under consideration, provided that a relatively small step size is employed. A wide variety of Abel’s integral equations is solved to demonstrate the applicability, accuracy, and stability of the proposed numerical algorithm. Encouraged by this success on the test problems, the proposed numerical method is applied to solve problems in electrochemistry, which are modeled by Abel’s integral equations. The obtained results confirm the practical appropriateness of the numerical algorithm for applications of Abel’s integral equations.
