<p>This paper presents a numerical method based on the modified Taylor wavelet (MTW) to solve the system of Abel integral equations. A direct operational matrix of integration based on MTW is employed to develop a suitable algorithm for the numerical inversion of the system of Abel integral equations. The main objective of using the MTW method is to transform the introduction problem into an equivalent set of algebraic equations. The applicability of the earlier proposed method was restricted to the numerical method of a part of the Abel integral equation. The method is quite accurate and stable, as illustrated by applying it to intensity data with or without random noise to approximate and compare it with the known analytical solution.</p>