A new numerical method to solve some \(\mathrm{PDE_s}\) in the unit ball and comparison with the finite element and the exact solution (Q2065046)

Summary: In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. We compare the results obtained using this approach to the standard finite element approach. The proposed method is adequate even with the singular right-hand side of type Dirac.