非线性反应扩散问题的高阶松弛格式
High order relaxed schemes for nonlinear reaction diffusion problems
AI总结：
本文通过耦合ENO/WENO空间离散与IMEX时间积分，提出高阶松弛格式用于非线性反应扩散方程的数值逼近，并在退化情形下验证了高精度和良好性质。
摘要：
最近，针对偏微分方程（包括守恒律、Hamilton-Jacobi方程、对流扩散问题、气体动力学问题）提出了不同的松弛近似。本文聚焦于非线性反应扩散方程数值逼近的扩散松弛格式。通过将ENO和WENO格式用于空间离散，与IMEX格式用于时间积分耦合，获得高阶方法，其中隐式部分可以以线性代价显式求解。为了说明所提数值格式的高精度和良好性质，包括退化情形，我们考虑了一维和二维中的多个例子：Fisher-Kolmogoroff方程、多孔Fisher方程和具有强吸收的多孔介质方程。
英文摘要：
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto diffusive relaxed schemes for the numerical approximation of nonlinear reaction diffusion equations. High order methods are obtained by coupling ENO and WENO schemes for space discretization with IMEX schemes for time integration, where the implicit part can be explicitly solved at a linear cost. To illustrate the high accuracy and good properties of the proposed numerical schemes, also in the degenerate case, we consider various examples in one and two dimensions: the Fisher-Kolmogoroff equation, the porous-Fisher equation and the porous medium equation with strong absorption.
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