Block-pulse functions approach to numerical solution of Abel's integral equation

This study aims to present a computational method for solving Abel's integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs) via collocation method. Abel's integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.