Restrictive Pade approximation and parabolic partial differential equations

In this paper, we use the restrictive Pade approximation to approximate the exponential matrix exp(rA). The advantage is that it has the exact value at certain r. We define a new accurate, fast implicit method for the finite difference solution of a parabolic partial differential equations. The stability region is discussed, the obtained results are compared with the exact solution and some famous finite difference methods. The numerical results are in satisfactory agreement with the exact solution.