In this paper, the $n$-dimensional stochastic Itô-Volterra integral equation is numerically solved via quintic B-spline collocation method. To reach this aim, the quintic B-spline interpolation, Gauss–Legendre quadrature formula and Itô approximation are presented. By using the quintic B-spline collocation method, $n$-dimensional stochastic Itô-Volterra integral equation can be reduced to a linear or nonlinear system of algebraic equations. Also, convergence analysis of the proposed method is discussed. Finally, it is used in some numerical examples to illustrate the effectiveness of the proposed method.

中文翻译：

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五次B样条搭配方法求解 $ñ$维随机Itô-Volterra积分方程

在本文中， $ñ$通过五次B样条搭配法对二维随机Itô-Volterra积分方程进行数值求解。为了达到这个目的，提出了五次B样条插值，高斯勒格朗德正交公式和Itô逼近。通过使用五次B样条搭配方法，$ñ$维随机Itô-Volterra积分方程可以简化为代数方程的线性或非线性系统。此外，讨论了该方法的收敛性分析。最后，在一些数值示例中使用它来说明所提方法的有效性。