Hybrid Methods in Engineering Modeling, Programming, Analysis, Animation

ISSN for PRINT: 1099-2391

For Online Access

Best Paper Award Selection - Editorial Board Site

2000, Volume2

Issue 1

132 pages

Issue price - $125.00

Abdulmajeed Mohamad
University of Calgary

The article addresses stability limits and accuracy of methods of advancing the solution of a system of ordinary differential equations (ODEs) in time by the Runge-Kutta (RK) and Taylor series (TS) methods. This system of ODEs arises as a result of discretizing the advection equation (a partial differential equation, PDE) spatially. Symbolic manipulation is used in the stability analysis. The Von Neumann linear stability method is illustrated with the aid of symbolic programming. The program is general and can be extended easily to analyze the stability of higher-order advection and advection-diffusion schemes. It is found that the RK and TS methods produce identical results as far as accuracy and stability limit are concerned. The TS method requires less memory storage than the RK method. Also, an explicit scheme based on the physics of the problem is constructed. The scheme is unconditionally stable and accurate for all values of Courant parameter.

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