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Convergence analysis of the hp-version spectral collocation method for a class of nonlinear variable-order fractional differential equations
- Source :
- Applied Numerical Mathematics. 170:269-297
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- In this paper, a general class of nonlinear initial value problems involving a Riemann-Liouville fractional derivative and a variable-order fractional derivative is investigated. An existence result of the exact solution is established by using Weissinger's fixed point theorem and Gronwall-Bellman lemma. An hp-version spectral collocation method is presented to solve the problem in numerical frames. The collocation method employs the Legendre-Gauss interpolations to conquer the influence of the nonlinear term and variable-order fractional derivative. The most remarkable feature of the method is its capability to achieve higher accuracy by refining the mesh and/or increasing the degree of the polynomial. The error estimates under the H 1 -norm for smooth solutions on arbitrary meshes and singular solutions on quasi-uniform meshes are derived. Numerical results are given to support the theoretical conclusions.
- Subjects :
- Numerical Analysis
Polynomial
Applied Mathematics
Fixed-point theorem
010103 numerical & computational mathematics
01 natural sciences
Fractional calculus
010101 applied mathematics
Computational Mathematics
Nonlinear system
Collocation method
Norm (mathematics)
Initial value problem
Applied mathematics
0101 mathematics
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 01689274
- Volume :
- 170
- Database :
- OpenAIRE
- Journal :
- Applied Numerical Mathematics
- Accession number :
- edsair.doi...........a0491f18eb348b998bdda985824a755d