The main aim of this study is presenting a semi-discretization scheme to find the numerical solution of two dimensional (2D) stochastic time fractional diffusion-wave equation, which obtains from classical 2D diffusion-wave equation by replacing integer time derivative with Caputo fractional time derivative of order α (1 < α ≤ 2) and inserting some stochastic factors. In this scheme, first Crank-Nicolson and linear spline techniques are used to discrete mentioned problem in the time direction and then Hermite-based approach is applied to obtain the approximate solution in each time step. It is not required any discretization in the spatial directions and therefore this approach is an efficient tool to solve various problems which have been defined on irregular domains. Finally, to confirm this claim that obtained numerical results are accurate and in reliable agreement with the theoretical discussion, some test problems are included in the numerical example section. The values of maximum error, error associated with norm 2, and RMS–error are reported to demonstrate accuracy and reliability of the proposed method. Also, the domain of last example is considered in a long range of the time interval to study the stability of our method on time variable.

这项研究的主要目的是提出一种半离散方案，以找到二维（2D）随机时间分数扩散波方程的数值解，该方程是通过用Caputo分数时间代替整数时间导数从经典的二维扩散波方程中获得的α阶导数（1 <  α ≤2）并插入一些随机因素。在该方案中，首先使用Crank-Nicolson和线性样条技术在时间方向上离散提到的问题，然后使用基于Hermite的方法在每个时间步中获得近似解。不需要在空间方向上进行任何离散化，因此此方法是解决在不规则域中定义的各种问题的有效工具。最后，为了确认所获得的数值结果准确且与理论讨论可靠一致的主张，数值示例部分中包含了一些测试问题。报告了最大误差，与范数2相关的误差和RMS-误差的值，以证明所提出方法的准确性和可靠性。也，