New predictor‐corrector scheme for solving nonlinear differential equations with Caputo‐Fabrizio operator
Copyright policy )New predictor‐corrector scheme for solving nonlinear differential equations with Caputo‐Fabrizio operator
In this paper, we develop a new, simple, and accurate scheme to obtain approximate solution for nonlinear differential equation in the sense of Caputo‐Fabrizio operator. To derive this new predictor‐corrector scheme, which suits on Caputo‐Fabrizio operator, firstly, we obtain the corresponding initial value problem for the differential equation in the Caputo‐Fabrizio sense. Hence, by fractional Euler method and fractional trapeziodal rule, we obtain the predictor formula as well as corrector formula. Error analysis for this new method is derived. To test the validity and simplicity of this method, some illustrative examples for nonlinear differential equations are solved.
- Tun Hussein Onn University of Malaysia Malaysia
- Taylor's University Malaysia
- Taylors University Malaysia
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Adams-Bashforth-Moulton method, Caputo fractional derivative, predictor-corrector scheme, Caputo-Fabrizio operator, T57-57.97 Applied mathematics. Quantitative methods, Fractional ordinary differential equations, nonlinear differential equation, 510, 620
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Adams-Bashforth-Moulton method, Caputo fractional derivative, predictor-corrector scheme, Caputo-Fabrizio operator, T57-57.97 Applied mathematics. Quantitative methods, Fractional ordinary differential equations, nonlinear differential equation, 510, 620
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