High-Order Algorithms for Riesz Derivative and Their Applications $(I)$

By Heng-fei Ding, Changpin Li, YangQuan Chen. 2014

148 citations recorded by the source corpus.

We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth-order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first-order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/18427783308cf5a958c3a49061146c5e8c177630

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Minhao Cai
2. Changpin Li

In Modeling and Simulation

1. Minhao Cai
2. Changpin Li
3. Weihua Deng
4. N. Kosmatov

In Numerical Analysis

1. Minhao Cai
2. Changpin Li

Citations in the corpus

• Numerical Approaches to Fractional Integrals and Derivatives: A Review (2020, background): “Weighted and shifted centred difference operators Introducing shifts to the symmetric fractional centred difference operator in Equation (267), the shifted centred difference operators [112]”