Moving collocation methods for time fractional differential equations and simulation of blowup
2011
A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.
Keywords:
- Stochastic partial differential equation
- Mathematical analysis
- Orthogonal collocation
- Method of characteristics
- FTCS scheme
- Separable partial differential equation
- Collocation method
- Mathematical optimization
- Mathematics
- Spectral method
- Numerical partial differential equations
- Differential algebraic equation
- Nonlinear system
- Differential equation
- Partial differential equation
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