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Krylov implicit integration factor method for a class of stiff reaction-diffusion systems with moving boundaries. (English) Zbl 1427.65172
Summary: The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population. There are several numerical difficulties to efficiently handle such systems. Firstly extremely small time steps are usually demanded due to the stiffness of the system. Secondly it is always difficult to efficiently and accurately handle the moving boundaries. To overcome these difficulties, we first transform the one-dimensional problem with a moving boundary into a system with a fixed computational domain, and then introduce four different temporal schemes: Runge-Kutta, Crank-Nicolson, implicit integration factor (IIF) and Krylov IIF for handling such stiff systems. Numerical examples are examined to illustrate the efficiency, accuracy and consistency for different approaches, and it can be shown that Krylov IIF is superior to other three approaches in terms of stability and efficiency by direct comparison.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
92D25 Population dynamics (general)
35R37 Moving boundary problems for PDEs
35K57 Reaction-diffusion equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L04 Numerical methods for stiff equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65F50 Computational methods for sparse matrices
65F60 Numerical computation of matrix exponential and similar matrix functions
Software:
MATLAB expm; RADAU
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References:
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