Walsh function-based numerical approach for nonlinear stochastic integral equations: Application to stochastic logistic models

Abstract

The current research study proposes an efficient numerical method for obtaining an approximate solution to nonlinear stochastic integral equations implementing the collocation method and the Walsh operational matrices. Given the complexity of solving each integral equation exactly, we use a numerical approach that converts the equation into a system of algebraic equations, yielding an approximate solution. Through error analysis, the method is found to exhibit linear convergence, underscoring its efficiency. We offer numerical tests to show the accuracy and usefulness of the proposed approach. This work also demonstrates the applicability of the method to dealing with the stochastic logistic model.