A Generalized NPCM for Solving Multi-Term Fractional Differential Equations

A new predictor-corrector method (NPCM) was developed by Daftardar-Gejji and Sukale et al. (Appl Math Comput 244: 158-182, 2014) to solve fractional order differential equations. In the present article, we develop a new algorithm for solving multi-term fractional differential equations. This new alg...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2022, Vol.8 (3), Article 115
Main Authors: Mahatekar, Yogita, Deshpande, Amey S.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Differential equations
Fractional calculus
Iterative methods
Mathematical analysis
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Predictor-corrector methods
Theoretical
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Summary:A new predictor-corrector method (NPCM) was developed by Daftardar-Gejji and Sukale et al. (Appl Math Comput 244: 158-182, 2014) to solve fractional order differential equations. In the present article, we develop a new algorithm for solving multi-term fractional differential equations. This new algorithm developed is effectively a generalization of NPCM for solving multi-term fractional differential equations and hence we refer to it as NPCM-MT. The new method NPCM-MT is a combination of implicit product trapezoidal rule and New Iterative Method (J Math Anal Appl 316(2): 753–763 2006). The NPCM-MT is compared with Fractional Adams Method (FAM) for multi-term fractional differential equations, and is found to be more time-efficient & accurate than FAM. Numerous illustrative examples are discussed here to demonstrate effectiveness of the NPCM-MT. Detailed convergence analysis of the method is given including error bounds under various types of assumptions on the equation.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-022-01305-5