Continuous symmetries of certain nonlinear partial difference equations and their reductions

Sahadevan, R.; Nagavigneshwari, G.

doi:10.1016/j.physleta.2014.09.021

Cited by 1 publication

(2 citation statements)

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“…Lie group theory is an efficient tool for solutions of differential equations [3]. It is also more convenient for the discretization of both ordinary differential equations (ODEs) [4][5][6] and partial differential equations (PDEs) [7][8][9]. For a given finite-difference equation (system), one can have the operators of the group admitted by the equation.…”

Section: Introductionmentioning

confidence: 99%

“…There have been some papers on constructing the invariant discretizations of dynamical systems based on the inverse problem method above, such as the one-dimensional gas systems [24], the shallow water equations in Lagrangian [25], the holonomic dynamical systems [23], etc. The symmetry preserving discretization of ODE and PDE are studied deeply [9,10,[19][20][21][22][23]. The theory has been applied to dynamical systems recently.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints

Xia

2021

Mathematics

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Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.

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