A significant group of mathematical issues known as Volterra integral equations appear in numerous scientific and engineering applications. These equations are inherently nonlinear and complicated, making analytical solution difficult. In order to solve Volterra integral equations of the first class, a novel analytical technique known as the Hussein Jassim Method (HJ-method) is presented in this research work. The Volterra integral equations are introduced mathematically in the first section of the study, which also emphasizes their importance in simulating real-world processes. The novel method’s algorithm is then described, followed by an analysis. We also research the novel method’s convergence characteristics and the circumstances under which it produces trustworthy results. We provide a number of Volterra integral equation examples to show the potency of this approach.
In the end, the new method has proven to be effective and efficient in solving first-kind Volterra integral equations. The method has produced satisfactory results, with the obtained solution closely approximating the exact solution. These findings indicate the capability of this method to address the mathematical and technical challenges associated with solving Volterra integral equations. This also makes it possible to use the new technique in other relevant practical contexts.