Numerical solution of fractional oscillator equation.(English)Zbl 1243.65090

Summary: We focus on a numerical scheme applied for a fractional oscillator equation in a finite time interval. This type of equation includes a complex form of left- and right-sided fractional derivatives. Its analytical solution is represented by a series of left and right fractional integrals and therefore is difficult in practical calculations. Here we elaborate two numerical schemes being dependent on a fractional order of the equation. The results of numerical calculations are compared with analytical solutions. Then we illustrate convergence and stability of our schemes.

MSC:

 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34A08 Fractional ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations
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References:

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