Fourth-order exponential time differencing Runge–Kutta scheme and local meshless method to investigate unsteady diffusion–convection problems of anisotropic functionally graded materials

The current article is devoted to proposing a local meshfree method for simulating the unsteady diffusion–convection problems of anisotropic functionally graded materials (AFGM). The first stage of the proposed numerical algorithm is based on discretizing the spatial variables by utilizing the direct meshless local Petrov–Galerkin (DMLPG) method. Then a system of ODEs is extracted which is associated to the time variable. Furthermore, the fourth-order exponential time differencing Runge–Kutta method is applied to solve the system of ODEs. The main aim of this work is to introduce a flexible and low-cost numerical procedure to solve unsteady diffusion–convection problems of AFGM on the complicated geometry. The new numerical technique has admissible resultants to simulate the studied model. This numerical formulation is applied to several examples with complex domains to check its ability.