Numerical solution of space-fractional partial differential equations by a differential quadrature approach
Provides a new numerical tool for solving space-fractional PDEs, but the method is incremental and requires careful parameter tuning.
The authors developed a differential quadrature method using radial basis functions to solve space-fractional PDEs, achieving high accuracy when shape parameters are properly chosen.
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted linear combinations of the function values at discrete grid points on problem domain with the weights calculated via using three types of radial basis functions (RBFs) as test functions. The method in presence is robust, straight forward to apply, and highly accurate under the condition that the shape parameters of RBFs are well chosen. Numerical tests are provided to illustrate its validity and capability.