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

Abstract

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.

KEYWORDS:

• Inhomogeneous parabolic PDEs
• real pole rational approximation
• computationally fast
• fractional distributed order PDEs
• Riesz derivative

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K20
• 35K58
• 35R11
• 65N40

Disclosure statement

No potential conflict of interest was reported by the author(s).