Implicit meshless method to solve <scp>2D</scp> fractional stochastic Tricomi‐type equation defined on irregular domain occurring in fractal transonic flow
Farshid Mirzaee, Nasrin Samadyar
Abstract
Abstract In the current paper, we develop a new method based on the finite difference formulation and meshless method to solve 2D time fractional stochastic Tricomi‐type equation with Caputo derivative in temporal direction and Neumann boundary condition defined on irregular domain, numerically. In this method, first the fractional order derivative is discretized by a finite difference scheme and then meshless method based on radial basis functions is employed to approximate the functions in the spatial directions. So, the solution of considered problem is transformed to the solution of a linear system of algebraic equations which will be solved at each time step. The most advantage of this method is that it has no triangular, quadrangular, or other type of meshes and therefore is very applicable to solve various high dimensional problems. Finally, some test problems with different domains have been solved via present method to verify the accuracy and efficiency of the newly developed meshless formulation. Numerical results confirm the present technique is very effective to approximate the solution of 2D fractional stochastic Tricomi‐type equation with Neumann boundary condition.