An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids (Q1931781)

The paper presents an adaptive Peaceman-Rachford splitting method for quenching-type problems in the form of degenerate reaction-diffusion equations on nonuniform grids. The authors employ a condition on the maximum step-size which is derived to ensure the positivity and monotonic property in the numerical solution. The condition relates to the minimum spatial step-size and the maximum value of the degenerate function. Weak stability is proved in a von Neumann sense via the infinite norm. Computation examples show good agreement with known theoretical and experimental results using fairly coarse grids.