scholarly journals A Compact Difference Scheme for Solving Fractional Neutral Parabolic Differential Equation with Proportional Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Wei Gu ◽  
Yanli Zhou ◽  
Xiangyu Ge
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Test ◽  
Unconditional Stability ◽  
Parabolic Differential Equation ◽  
Proportional Delay ◽  
Compact Difference Scheme ◽  
Compact Finite Difference Scheme ◽  
Compact Difference

A linearized compact finite difference scheme is constructed for solving the fractional neutral parabolic differential equation with proportional delay. By the energy method, the unconditional stability of the scheme is proved, and the convergence order of the scheme is proved to be O(τ2-α+h4). A numerical test is also conducted to validate the accuracy and efficiency of the numerical algorithm.

A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shufang Hu ◽  
Wenlin Qiu ◽  
Hongbin Chen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Compact Finite Difference Scheme ◽  
Compact Finite Difference ◽  
Integro Differential Equation ◽  
Compact Finite Difference Method ◽  
Backward Euler ◽  
Predictor Corrector

Abstract A predictor–corrector compact finite difference scheme is proposed for a nonlinear partial integro-differential equation. In our method, the time direction is approximated by backward Euler scheme and the Riemann–Liouville (R–L) fractional integral term is treated by means of first order convolution quadrature suggested by Lubich. Meanwhile, a two-step predictor–corrector (P–C) algorithm called MacCormack method is used. A fully discrete scheme is constructed with space discretization by compact finite difference method. Numerical experiment presents the scheme is in good agreement with the theoretical analysis.

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.

scholarly journals A Compact Difference Scheme for a Class of Variable Coefficient Quasilinear Parabolic Equations with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wei Gu
Keyword(s):  
Difference Scheme ◽  
Variable Coefficient ◽  
Numerical Test ◽  
Parabolic Systems ◽  
Stability And Convergence ◽  
Compact Difference Scheme ◽  
Quasilinear Parabolic Equations ◽  
Compact Difference ◽  
The Difference ◽  
Equations With Delay

A linearized compact difference scheme is provided for a class of variable coefficient parabolic systems with delay. The unique solvability, unconditional stability, and convergence of the difference scheme are proved, where the convergence order is four in space and two in time. A numerical test is presented to illustrate 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
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