scholarly journals Fourth-Order Compact Difference Schemes for the Riemann-Liouville and Riesz Derivatives

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yuxin Zhang ◽  
Hengfei Ding ◽  
Jincai Luo
Keyword(s):  
Fourth Order ◽  
Numerical Approximation ◽  
Difference Schemes ◽  
Order Convergence ◽  
Transform Method ◽  
Numerical Examples ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
The Fourier Transform ◽  
Convergence Orders

We propose two new compact difference schemes for numerical approximation of the Riemann-Liouville and Riesz derivatives, respectively. It is shown that these formulas have fourth-order convergence order by means of the Fourier transform method. Finally, some numerical examples are implemented to testify the efficiency of the numerical schemes and confirm the convergence orders.

Simulating waves in flows by Runge-Kutta and compact difference schemes

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 421-429 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Kwang-Chung Hsieh ◽  
Y.-L. Peter Tsai
Keyword(s):  
Difference Schemes ◽  
Compact Difference Schemes ◽  
Compact Difference ◽  
Runge Kutta

An Accelerated Iterative Method with Third-Order Convergence

2012 ◽  
Vol 220-223 ◽  
pp. 2658-2661
Author(s):  
Zhong Yong Hu ◽  
Liang Fang ◽  
Lian Zhong Li
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Newton's Method ◽  
New Method ◽  
Order Convergence ◽  
Third Order ◽  
Numerical Examples ◽  
Modified Newton’S Method ◽  
Jarratt Method

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

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