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 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.

scholarly journals Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Fadime Dal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Mixed Problem ◽  
Variational Iteration Method ◽  
Analytic Solutions ◽  
Hyperbolic Partial Differential Equations ◽  
Neumann Condition ◽  
Stability Estimates ◽  
Partial Differential

The numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation with the Neumann condition is presented. Stability estimates for the solution of this difference scheme and for the first- and second-order 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. He's variational iteration method is applied. The comparison of these methods is presented.

scholarly journals A Stable Difference Scheme for a Third-Order Partial Differential Equation

2018 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
A Ashyralyev ◽  
Kh Belakroum
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.

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.

scholarly journals Oscillation criteria for high order delay partial differential equations

1998 ◽  
Vol 11 (2) ◽  
pp. 193-208 ◽  
Author(s):  
Xinzhi Liu ◽  
Xilin Fu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
High Order ◽  
Differential Inequalities ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Different Boundary Conditions ◽  
Delay Differential ◽  
Delay Partial Differential Equations

This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

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