Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods

Shaher Momani, Zaid Odibat, Ishak Hashim

DOI: http://dx.doi.org/10.12775/TMNA.2008.012

Abstract


Fractional order partial differential equations, as
generalization of classical integer order partial differential
equations, are increasingly used to model problems in fluid flow,
finance and other areas of applications. In this paper we present
a collection of numerical algorithms for the solution of nonlinear
partial differential equations with space- and time-fractional
derivatives. The fractional derivatives are considered in the Caputo
sense. Two numerical examples are given to demonstrate the
effectiveness of the present methods. Results show that
the numerical schemes are very effective and convenient
for solving nonlinear partial differential equations of fractional
order.

Keywords


Fractional differential equations; differential transform method; homotopy perturbation method; variational iteration method; Adomian decomposition method

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