Physics – Computational Physics
Scientific paper
2007-05-08
Physics
Computational Physics
48 pages, 6 figures. Found inexactitudes are corrected. A second order scheme based on operator-splitting techniques is constr
Scientific paper
The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability of the corresponding non-linear scheme. The main methodological innovation is the theorems establishing the notion that a non-linear scheme is stable (and monotone) if the corresponding scheme in variations is stable (and, respectively, monotone). Criteria are developed for monotonicity and stability of difference schemes associated with the numerical analysis of systems of partial differential equations. The theorem of Friedrichs (1954) is generalized to be applicable to variational schemes with non-symmetric matrices. A new modification of the central Lax-Friedrichs (LxF) scheme is developed to be of the second order accuracy. A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The stability and monotonicity of the modified scheme are investigated. Some versions of the modified scheme are tested on several conservation laws, and the scheme is found to be accurate and robust. As applied to hyperbolic conservation laws with, in general, stiff source terms, it is constructed a second order scheme based on operator-splitting techniques.
Borisov Vyacheslav S.
Mond Michael
No associations
LandOfFree
On monotonicity, stability, and construction of central schemes for hyperbolic conservation laws with source terms (Revised Version) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On monotonicity, stability, and construction of central schemes for hyperbolic conservation laws with source terms (Revised Version), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On monotonicity, stability, and construction of central schemes for hyperbolic conservation laws with source terms (Revised Version) will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-153810