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 initi...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 42; no. 1; pp. 175 - 185
Main Authors Toh, Yoke Teng, Phang, Chang, Loh, Jian Rong
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.01.2019
Subjects
Adams‐Bashforth‐Moulton method
Boundary value problems
Caputo fractional derivative
Caputo‐Fabrizio operator
Error analysis
Error correction
Formulas (mathematics)
Mathematical analysis
nonlinear differential equation
Nonlinear differential equations
Nonlinear equations
Operators (mathematics)
Predictor-corrector methods
predictor‐corrector scheme
Test procedures
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5331