A stable numerical scheme for solving heat transport equations on the microscopic and cracked domains

The numerical computation of the thermal behavior of microstructures in partial differential equations on various regions such as the microscopic region where the thickness is at the sub-microscale or complex and cracked domains are considered. Initially, a Taylor series expansion is used, and structural assumptions are made on the problem to eliminate heat flux and, consequently derive a dimensionless heat transport equation. Starting from the heat transport equation with initial and boundary conditions (IBCs), we study a meshless method and in some detail a basic model of trigonometric basis functions (TBFs). Finally, the method is supported by several numerical experiments.