English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The monotonicity and stability of difference schemes for, in general,hyperbolic systems of conservation laws with source terms are studied. Thebasic approach is to investigate the stability and monotonicity of a non-linearscheme in terms of its corresponding scheme in variations. Such an approachleads to application of the stability theory for linear equation systems toestablish stability of the corresponding non-linear scheme. The mainmethodological innovation is the theorems establishing the notion that anon-linear scheme is stable (and monotone) if the corresponding scheme invariations is stable (and, respectively, monotone). Criteria are developed formonotonicity and stability of difference schemes associated with the numericalanalysis of systems of partial differential equations. The theorem ofFriedrichs (1954) is generalized to be applicable to variational schemes withnon-symmetric matrices. A new modification of the central Lax-Friedrichs (LxF)scheme is developed to be of the second order accuracy. A monotone piecewisecubic interpolation is used in the central schemes to give an accurateapproximation for the model in question. The stability and monotonicity of themodified scheme are investigated. Some versions of the modified scheme aretested on several conservation laws, and the scheme is found to be accurate androbust. As applied to hyperbolic conservation laws with, in general, stiffsource terms, it is constructed a second order scheme based onoperator-splitting techniques.

On monotonicity, stability, and construction of central schemes for hyperbolic conservation laws with source terms (Revised Version)