A simulation expressivity of the quenching phenomenon in a two-sided space-fractional diffusion equation

Highlights：

• The solution stability, monotonicity and positivity are rigorously analyzed, proved, and validated through sequences of simulation experiments.

• α∈[(17−1)/2,2)Two interconnected sets of simulation experiments are designed and presented. They demonstrate the correctness and accuracy of the approximation of the solution of two-sided fractional differential equation. The experiments also indicate that solutions of the two-sided fractional model may provide more balanced and accurate interpretation of the quenching phenomena as compared with conventional fractional equations.

摘要

•A novel numerical method for a quenching type diffusion equation associated with a two-sided Riemann-Liouville spatially fractional derivative is studied. The Crank-Nicolson type scheme, equipped with a temporal arc-length adaptation strategy ensuring additional accuracy and reliability for capturing the singular solution of the fractional Kawarada modeling equation, is highly effective.•The solution stability, monotonicity and positivity are rigorously analyzed, proved, and validated through sequences of simulation experiments.•α∈[(17−1)/2,2)Two interconnected sets of simulation experiments are designed and presented. They demonstrate the correctness and accuracy of the approximation of the solution of two-sided fractional differential equation. The experiments also indicate that solutions of the two-sided fractional model may provide more balanced and accurate interpretation of the quenching phenomena as compared with conventional fractional equations.