scholarly journals A linearized compact difference scheme for a class of nonlinear delay partial differential equations

2013 ◽  
Vol 37 (3) ◽  
pp. 742-752 ◽  
Author(s):  
Zhi-zhong Sun ◽  
Zai-bin Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Compact Difference Scheme ◽  
Partial Differential ◽  
Compact Difference ◽  
Delay Partial Differential Equations ◽  
Nonlinear Delay

scholarly journals On the Absolute Stable Difference Scheme for Third Order Delay Partial Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1033
Author(s):  
Allaberen Ashyralyev ◽  
Evren Hınçal ◽  
Suleiman Ibrahim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Stability Estimates ◽  
Third Order ◽  
Partial Differential ◽  
The Absolute ◽  
The Stability ◽  
Delay Differential ◽  
Delay Partial Differential Equations

The initial value problem for the third order delay differential equation in a Hilbert space with an unbounded operator is investigated. The absolute stable three-step difference scheme of a first order of accuracy is constructed and analyzed. This difference scheme is built on the Taylor’s decomposition method on three and two points. The theorem on the stability of the presented difference scheme is proven. In practice, stability estimates for the solutions of three-step difference schemes for different types of delay partial differential equations are obtained. Finally, in order to ensure the coincidence between experimental and theoretical results and to clarify how efficient the proposed scheme is, some numerical experiments are tested.

scholarly journals A Crank-Nicolson Difference Scheme for Solving a Type of Variable Coefficient Delay Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Gu ◽  
Peng Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Variable Coefficient ◽  
Numerical Test ◽  
Partial Differential ◽  
The Difference ◽  
Delay Partial Differential Equations ◽  
Theoretical Results ◽  
Crank Nicolson

A linearized Crank-Nicolson difference scheme is constructed to solve a type of variable coefficient delay partial differential equations. The difference scheme is proved to be unconditionally stable and convergent, where the convergence order is two in both space and time. A numerical test is provided to illustrate the theoretical results.

Impact on Partial Differential Equations Filtering Models of Difference Scheme

2015 ◽  
Vol 52 (9) ◽  
pp. 091004
Author(s):  
王琳霖 Wang Linlin ◽  
唐晨 Tang Chen ◽  
王亚杰 Wang Yajie
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Partial Differential

scholarly journals On the Numerical Solution of Fractional Hyperbolic Partial Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fadime Dal ◽  
Zehra Pinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Hyperbolic Partial Differential Equations ◽  
Stability Estimates ◽  
Partial Differential ◽  
One Dimensional ◽  
Gauss Elimination ◽  
Gauss Elimination Method

The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation is presented. Stability estimates for the solution of this difference scheme and for the first and second orders difference derivatives are obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional hyperbolic partial differential equations.

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