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Validation and calibration of models for reaction-diffusion systems. (English) Zbl 1040.65085
The authors introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite \(\Delta x\) and \(\Delta t\), if the ratio \(\gamma_N = D \Delta t/(\Delta x)^2\) assumes a fixed constant value. With these integration methods anisotropy effects resulting from the finite differences are minimized. Comparisons between numerical and analytical solutions of reaction-diffusion equations give convincing small global discretization errors.

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
Software:
PDE2D
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