2024 , Volume 29, № 5, p.55-71

Our overarching goal is to significantly enhance computational efficiency and minimize memory space utilization which is very important in the case of large integration intervals. To begin this endeavor, we establish sufficient conditions that guarantee the existence and uniqueness of the solution. Our novel method is grounded in the Single Equation Approach, which consists in using the variable transformation 𝑣(𝑥), completed by the Trapezoidal rule. This transformation plays a pivotal role in converting our equation into an algebraic system, thereby reducing the number of equations and unknowns in the discrete system. Underlying these developments is a fundamental requirement ensuring the existence and uniqueness of the solution. Leveraging this, we formulate theorems that establish the convergence of the approximate solution, ensuring consistency between analytical and numerical investigations. Ultimately, we conduct a comparative analysis between our newly introduced technique and the older method. This comparison serves to highlight the superior computational efficiency and reduced storage space consumption offered by our innovative digital framework.