Spectral collocation methods for nonlinear coupled time fractional Nernst-Planck equations in two dimensions and its convergence analysis. (English) Zbl 1442.65300
Summary: In this paper, a nonlinear coupled time fractional Nernst-Planck equation in two dimensions space is considered. Using properties of the Caputo fractional derivative and Riemann-Liouville fractional integral, the time fractional Nernst-Planck problem is transformed into a Volterra integral model with singular kernel equivalently. We propose a novelty spectral collocation method in time and space with a spectral expansion of Jacobi interpolation polynomial to discretize the model. We also derive the optimal rate of convergence of this method. Numerical results are presented to verify efficiency of collocation methods and spectral accuracy theory.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
time fractional Nernst-Planck equation; nonlinear coupling; spectral collocation method; convergenceReferences:
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