论文标题
分数扩散的双指数正交
Double exponential quadrature for fractional diffusion
论文作者
论文摘要
我们基于双指数正交公式和riesz-dunford函数积分，为椭圆形和抛物线分数扩散问题引入了一种新颖的离散技术。与相关方案相比，新方法提供了更快的收敛性，而较少的参数需要调整到问题。该方案利用问题中的任何额外平滑度，而无需适当地调整参数。我们证明了两者的严格合并结果，即有限的规律性数据以及某些Gevrey类型类中的数据。我们通过数值测试确认我们的发现。
We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new method provides faster convergence with fewer parameters that need to be adjusted to the problem. The scheme takes advantage of any additional smoothness in the problem without requiring a-priori knowledge to tune parameters appropriately. We prove rigorous convergence results for both, the case of finite regularity data as well as for data in certain Gevrey-type classes. We confirm our findings with numerical tests.
