This talk begins with a very brief introduction of the Fractional Calculus theory, focusing mainly on the analysis and numerical approximation of fractional differential equations. The main part of this talk will consist on the presentation of a nonpolynomial collocation method for the numerical approximation to the solution of this kind of equations. Initial and boundary (or terminal) value problems will be distinguished. An outline of the proof of the convergence order of these numerical schemes is provided and illustrated with some numerical results.
References
N. J. Ford, M. L. Morgado and M. Rebelo, Nonpolynomial collocation approximation of solutions
to fractional differential equations, Fract. Calc. Appl. Anal., in press.
N. J. Ford, M. L. Morgado and M. Rebelo, High order numerical methods for fractional terminal
value problems, Comp. Meth. in Appl. Math., in press. doi: 10.1515/cmam-2013-0022 |