A fast third order algorithm for two dimensional inhomogeneous fractional parabolic partial differential equations

A computationally fast third order numerical algorithm is developed for inhomogeneous parabolic partial differential equations. The algorithm is based on a third order method developed by using a rational approximation with single Gaussian quadrature pole to avoid complex arithmetic and to achieve high efficiency and accuracy. Difficulties with computational efficiency and accuracy are addressed using partial fraction decomposition technique. Third order accuracy and convergence of the method is proved analytically and verified numerically. Several classical as well as more challenging fractional and distributed order inhomogeneous problems are considered to perform numerical experiments. Computational efficiency of the method is demonstrated through central processing unit (CPU) time and is given in the convergence tables.