Development of a computational approach for a space-time fractional moving boundary problem arising from drug release systems. (English) Zbl 1476.65170
Summary: This paper presents an iterative procedure based on an implicit finite difference method to solve a mathematical model of drug delivery from a planar matrix with a moving boundary condition. This model includes the diffusion equation with space-time fractional-order derivatives. We establish the stability and convergence analysis of the method. We compare the numerical results with the scale-invariant and the homotopy perturbation solutions for different space-time-fractional orders and the problem parameters.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 92-08 | Computational methods for problems pertaining to biology |
Keywords:
fractional diffusion equation; moving boundary; variable time-grid method; Caputo derivativeReferences:
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