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An algorithm for the numerical solution of nonlinear fractional-order van der Pol oscillator equation. (English) Zbl 1255.65142

Summary: This paper is devoted to the numerical simulation for solving a special class of fractional differential equations. Based on the Grünwald-Letnikov definition of a fractional derivative, a numerical scheme for the approximation of the solution is discussed. By using this scheme, we solve the fractional Van der Pol equation. The results obtained here compare well with the analytical solutions and this shows that the numerical scheme is stable.

MSC:

65L12 Finite difference and finite volume methods for ordinary differential equations
34A08 Fractional ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
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