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 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 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 Application of Variational Iteration Method to Fractional Hyperbolic Partial Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Fadime Dal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Variational Iteration ◽  
Gauss Elimination ◽  
Gauss Elimination Method ◽  
Iteration Technique

The solution of the fractional hyperbolic partial differential equation is obtained by means of the variational iteration method. Our numerical results are compared with those obtained by the modified Gauss elimination method. Our results reveal that the technique introduced here is very effective, convenient, and quite accurate to one-dimensional fractional hyperbolic partial differential equations. Application of variational iteration technique to this problem has shown the rapid convergence of the sequence constructed by this method to the exact solution.

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