Numerical performance of some positivity preserving methods for the diffusion equation where the diffusion coefficient depends on both time and space
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Keywords:
Diffusion, Heat Conduction Unconditionally Stable Numerical Methods, Positivity Preserving SchemesAbstract
The transient diffusion equation is solved, where the diffusion coefficient itself depends
simultaneously on space and time. A nontrivial analytical solution containing the Whittaker functions is
reproduced by 15 explicit numerical time integrators, most of which unconditionally preserve the positivity
of the solutions. The accuracy of the methods is extensively examined, and it is found that these algorithms
give very good results even in those cases where the standard explicit Runge-Kutta methods are hopeless
due to the extreme stiffness of the problem.
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