Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System

2014 ◽  
Vol 6 (4) ◽  
pp. 419-435 ◽  
Author(s):  
Seakweng Vong ◽  
Zhibo Wang
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
High Order ◽  
Compact Difference Scheme ◽  
Compact Finite Difference Scheme ◽  
Numerical Examples ◽  
First Order ◽  
Compact Difference ◽  
High Order Convergence ◽  
Theoretical Results

AbstractIn this paper, we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system. We consider the situation in which the unknown function and its first-order derivative are given at the boundary. The scheme is shown to have high order convergence. Numerical examples are given to verify the theoretical results.

Direct calculation of waves in fluid flows using high-order compact difference scheme

AIAA Journal ◽  
1994 ◽  
Vol 32 (9) ◽  
pp. 1766-1773 ◽  
Author(s):  
Sheng-Tao Yu ◽  
Lennart S. Hultgren ◽  
Nan-Suey Liu
Keyword(s):  
Difference Scheme ◽  
Fluid Flows ◽  
Direct Calculation ◽  
High Order ◽  
Compact Difference Scheme ◽  
Compact Difference

scholarly journals High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Yongbin Ge
Keyword(s):  
Difference Scheme ◽  
Multigrid Method ◽  
Elliptic Problems ◽  
High Order ◽  
Compact Difference Scheme ◽  
Central Difference ◽  
Present Scheme ◽  
Compact Difference ◽  
Compact Approximations ◽  
Error Terms

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

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