Comparing Numerical Methods for Solving Nonlinear Fractional Order Differential Equations
This paper is a result of comparison of some available numerical methods for solving nonlinear fractional order ordinary differential equations. These methods are compared according to their computational complexity, convergence rate, and approximation error. The present study shows that when these methods are applied to nonlinear differential equations of fractional order, they have different convergence rate and approximation error.
- 4.Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent. Geophys J Roy Astr Soc 13:529–539Google Scholar
- 8.Diethelm K, Ford NJ, Freed (2002) A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam 29:3–22Google Scholar
- 10.Ford NJ, Simpson (2001) The numerical solution of fractional differential equations: speed versus accuracy. Numer Algorithms 26:336–346Google Scholar
- 11.Ford NJ, Connolly JA (2008) Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations. J Comput Appl Math. doi:10.1016/ j.cam.2008.04.003Google Scholar
- 13.Ichise M, Nagayanagi Y, Kojima T (1971) An analog simulation of non-integer order transfer functions for analysis of electrode process. J. Electroanal Chem 33:253–265Google Scholar
- 22.Vanloan CF (2000) Introduction to scientific computing: a Matrix-Vector Approach using MATLAB. Prentice-Hall, New JerseyGoogle Scholar