An efficient numerical approach for solving caputo fractional nonlinear two-point boundary value problems
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- An efficient numerical approach for solving caputo fractional nonlinear two-point boundary value problems
- Lee, Junseo
- Jang, Bongsoo
- Capuoto fractional derivative; Fractional differential equation; Fractional order boundary value problem; predictor-corrector methods; Nonlinear shooting methods
- Issue Date
- Graduate School of UNIST
- This paper proposed a new type of numerical scheme for solving Multi-term Fractional Nonlinear Differential Equation with Two Point Boundary Value Problems(FBVP).
The proposed methods take lower computational cost than conventional methods. In new techniques, the FBVP transposes to the System of Fractional Nonlinear Initial Value Problems(FIVP). In order to solve the system of FIVP, the Higher-Order Predictor-Corrector Method(HOM) is applied. Moreover, we employ shooting method based on Newton's and Halley's methods to approximate the unknown initial values of the system. Several numerical experiments show that the proposed methods give the same rate of convergence in the HOM.
- Department of Mathematical Sciences
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