High order numerical methods for fractional terminal value problems. (English) Zbl 1285.65049
Summay: We present a shooting algorithm to solve fractional terminal (or boundary) value problems. We provide a convergence analysis of the numerical method, derived based upon properties of the equation being solved and without the need to impose smoothness conditions on the solution. The work is a sequel to our recent investigation where we constructed a nonpolynomial collocation method for the approximation of the solution to fractional initial value problems. Here we show that the method can be adapted for the effective approximation of the solution of terminal value problems. Moreover, we compare the efficiency of this numerical scheme against other existing methods.
MSC:
65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
34A08 | Fractional ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
65L20 | Stability and convergence of numerical methods for ordinary differential equations |