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Home  >  Volume 22 (2012)

Stabilization of product of eigen-values from difference scheme for the solution of hyperbolic equation by Odio Augustine Onyejuwa Volume 22 (November, 2012), pp 373 – 376
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Abstract

This paper is on stabilization of product of eigen-values from difference scheme for the solution of hyperbolic equation. We consider a suitable difference equation usually called a leap – frog scheme given as,

 . Here, U depends on the time and space variables and  is a real constant. U is also differentiable in its domain of definition. Because of these properties of U, U is called an admissible function and we then apply the Taylor series expansion on it. By using trial solution for the Von Neumann method for the solution of the hyperbolic equation, we obtained the amplification matrix G(∆t,k) whose product of eigen-values of the characteristics equation for G(∆t,k) is less than one. Hence, this result shows that, the difference scheme is stable. 

Keywords: Stabilization, Eigen-values, difference scheme, courant number, Von-Neumann, admissible function and symmetric matrix.   

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