Numerical solution for two-dimensional partial differential equations using SM’s method

Abstract In this research paper, the authors aim to establish a novel algorithm in finite difference method (FDM). The idea is proposed mesh generation process, process generate random grids. FDM over randomly generated grid enables fast convergence and improves accuracy of solution for given problem; it also enhances quality precision by minimizing error. involves uniform grids, which are commonly used solving partial differential equation (PDE) fractional equation. However, requires higher number iterations reach convergence. addition, there still no definite principle discretization model mesh. newly method, SM employed grids generation. This compared with check validity potential computational time comparative study conducted first generating meshes different cell sizes, i.e. , 10 × , 20 30 40 10\times 10,\hspace{.25em}20\times 20,\hspace{.25em}30\times 30,\hspace{.25em}40\times 40 using MATLAB ANSYS programs. two-dimensional PDEs solved A significant reduction noticed. Thus, recommended be PDEs.