Delta basis functions and their applications to systems of integral equations

In the present paper, delta functions (DFs) are proposed as a new set of basis functions. Their properties and relations to well-known triangular functions (TFs) are described. The simplicity and useful properties of newly proposed sets led us to use them with more accuracy and less computational burden.Furthermore, DFs are applied to propose an efficient method for approximating the solution of integral equations systems. Convergence analysis and the rate of convergence have been considered as well. Some numerical examples are provided to illustrate the computational efficiency and accuracy of the method.