Book ChapterDOI
A Multicomponent Alternating Direction Method for Numerical Solution of Boussinesq Paradigm Equation
Natalia Kolkovska,Krassimir Angelow +1 more
- pp 371-378
Reads0
Chats0
TLDR
A vector of the discrete solutions to these schemes is found and it is proved that these discrete solutions converge to the continuous solution in the uniform mesh norm with O|h|2i¾?+i½?i¼?Abstract:
We construct and analyze a multicomponent alternating direction method a vector additive scheme for the numerical solution of the multidimensional Boussinesq Paradigm Equation BPE In contrast to the standard splitting methods at every time level a system of many finite difference schemes is solved Thus, a vector of the discrete solutions to these schemes is found It is proved that these discrete solutions converge to the continuous solution in the uniform mesh norm with O|h|2i¾?+i¾?i¾? order The method provides full approximation to BPE and is efficient in implementation The numerical rate of convergence and the altitudes of the crests of the traveling waves are evaluatedread more
Citations
More filters
Book ChapterDOI
Error Estimates of Four Level Conservative Finite Difference Schemes for Multidimensional Boussinesq Equation
TL;DR: It is proved that the discrete solution of the FDS converges to the exact solution with a second order of convergence with respect to space and time mesh steps in the first discrete Sobolev norm and in the uniform norm.
Proceedings ArticleDOI
Numerical computation of the critical energy constant for two-dimensional Boussinesq equations
Natalia Kolkovska,K. Angelow +1 more
TL;DR: In this article, a method for numerical evaluation of the critical energy constant in the multi-dimensional case by computing the ground state is proposed, and many numerical results are discussed and demonstrated.
Journal ArticleDOI
Comparison between two numerical methods for solution of 2D Boussinesq paradigm equation
TL;DR: In this paper , two numerical methods are used to obtain solution for the BPE, i.e., a Conservative Finite Difference Scheme (FDS) and a Taylor Series (TS) expansions around the time variable t. The results of the energy and the mass of the solution are compared.
References
More filters
Book
The Theory of Difference Schemes
TL;DR: The theory of difference schemes was introduced in this paper, where homogeneous difference schemes and different schemes for elliptic and time-dependent equations with constant coefficients were studied. And the theory of differenceschemes symbols was discussed.
MonographDOI
Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs
BookDOI
Numerical methods and applications
TL;DR: In this article, Dyakonov and Kobelkov proposed iterative methods based on linearization for nonlinear elliptic grid systems, E.G. Lebedev and A.V. Knyazev proposed a method to solve Stiff Systems of Differential Equations by Explicit Methods.
Journal ArticleDOI
An energy-consistent dispersive shallow-water model
TL;DR: In this article, a Boussinesq model for the flow of inviscid liquid in a shallow layer with free surface is revisited and a new localized solution is obtained analytically.