论文标题
在钢化部分偏微分方程的高阶方案上
On high-order schemes for tempered fractional partial differential equations
论文作者
论文摘要
在本文中，我们建议基于回火的分数扩散方程的加权和转移的Grünwald差异（回火WSGD）操作员，提出了空间中的三阶半差异方案。我们还显示了基于曲柄的完全离散方案的稳定性和收敛分析。还提出了针对钢化黑色 - choles方程的三阶方案，并通过数值进行了测试。进行了一些数值实验，以确认这些提出的方法的准确性和有效性。
In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grünwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and convergence analysis for the fully discrete scheme based a Crank--Nicolson scheme in time. A third-order scheme for the tempered Black--Scholes equation is also proposed and tested numerically. Some numerical experiments are carried out to confirm accuracy and effectiveness of these proposed methods.
