یک روش اختلاف فوری محدود برای معادلات دیفرانسیل جزئی فضای کسر توزیع شده در حوزه های محدب

Fast numerical methods were previously developed for space-fractional PDEs on multidimensional rectangular domains, without resorting to lossy compression, but rather, via the exploration of the tensor-product form of the Toeplitz-like decompositions of the stiffness matrices. In this paper we develop a fast finite difference method for distributed-order space-fractional PDEs on a general convex domain in multiple space dimensions. The fast method has an optimal order storage requirement and almost linear computational complexity, without any lossy compression. Numerical experiments show the utility of the method.