This article proposes an efficient numerical method for solving nonlinear stochastic Volterra integral equations using the operational matrices of the Walsh function and the collocation method. In this method, a nonlinear stochastic Volterra integral equation is reduced to a system of algebraic equations, which are then solved to obtain an approximation of the solution. Error analysis has been performed, confirming the effectiveness of the methodology, which results in a linear order of convergence. Examples were computed to demonstrate the efficacy and precision of the method.

翻译：本文提出了一种利用Walsh函数运算矩阵与配置法求解非线性随机Volterra积分方程的高效数值方法。该方法将非线性随机Volterra积分方程转化为代数方程组，通过求解该方程组获得解的近似值。误差分析表明该方法具有线性收敛阶，验证了其有效性。数值算例进一步展示了该方法的精确性与计算效率。