Finite Difference Methods for Fractional Differential Equations

Course Description

This course aims at providing the essential concepts and techniques that underlie the development and analysis of finite difference methods for fractional differential equations. Topics include introduction of fractional calculus, derivation of finite difference approximations of fractional derivatives, Grunwald difference formula, schemes for fractional ordinary differential equations, energy method for {it a priori} bounds of approximate solutions, analysis of stability, convergence and accuracy, applications to fractional partial differential equations with time-fractional and/or spatial-fractional derivatives. Recent development in this area will also be included.



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