On high order numerical schemes for fractional differential equations by block-by-block approach. (English) Zbl 1510.65164
Summary: The exact solutions to nonlinear fractional problems usually have initial singularity. Taking the singularity into account, the change of variable and the block-by-block approach are introduced to propose a novel high-order scheme. It is proved that our proposed scheme can be of order \(3 + \alpha\) under the non-smooth solutions. Numerical examples are shown to validate our theoretical results.
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
Keywords:
nonlinear fractional differential equation; high order scheme; convergence; non-smooth solutionReferences:
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