New insight into meshless radial point Hermite interpolation through direct and inverse 2-D reaction-diffusion equation

In this paper, we propose an effective method to solve partial differential equations dependent on time with Neumann boundary condition, by examining its effectivity on direct and inverse reaction-diffusion equation. This method merges the radial point interpolation and the Hermite-type interpolation techniques to provide us suitable tools to impose the boundary condition. This technique is called meshless radial point Hermite interpolation "MRPHI" which utilizes the radial basis function and its derivative to prepare suitable shape functions that are the key for expanding the high-order derivative. This procedure is tested on some types of two-dimensional diffusion equations to show stability through the time in different arbitrary domains.