A New Difference Scheme for Hyperbolic Partial Differential Equations

2017 ◽  
Author(s):  
Gaochang Zhao ◽  
Kewei Jie ◽  
Jie Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Hyperbolic Partial Differential Equations ◽  
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.

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.

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