APPLICATION OF REPRODUCING KERNEL ALGORITHM FOR SOLVING DIRICHLET TIME-FRACTIONAL DIFFUSION-GORDON TYPES EQUATIONS IN POROUS MEDIA

Time-fractional partial differential equations describe different phenomena in statistical physics, applied mathematics, and engineering. In this article, we propose and analyze an efficient reproducing kernel algorithm for the numerical solutions of such equations in porous media with Dirichlet boundary conditions. The representation of the exact and the numerical solutions is given in the W (Omega) and H (Omega) inner product spaces, whereas the computation of the required grid points relies on the R-(y,R- s) (x, t) and r((y, s)) (x, t) reproducing kernel functions. To confirm the accuracy of the new approach, several numerical examples are implemented, including linear and nonlinear terms that are acquired by interrupting the n-term of the exact solutions. The convergence of the utilized algorithm is studied theoretically and numerically by comparing the exact solutions of the problems under investigation. Finally, the obtained results show the significant improvement of the algorithm while saving the convergence accuracy and time.