The convergence of fully discrete Galerkin approximations of the Rosenau equation

Lee, H. Y.; Ohm, Mi Ray; Shin, Jun Yong

doi:10.1007/bf02941903

Cited by 15 publications

(2 citation statements)

References 2 publications

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“…In , Mittal et al have developed a collocation method for solving some Roseneu‐type nonlinear higher order evolution equation with Dirichlet boundary conditions using quintic B‐splines basis functions. Convergence of the semidiscrete solution of the Rosenau Equation and Rosenau‐RLW Equation and the error analysis of the modified Galerkin–Crank–Nicolson method has been studied in . Recently, many conservative difference methods for the Rosenau Equation also exists in the literature see and the references therein.…”

Section: Introductionmentioning

confidence: 99%

New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves

Ghiloufi

Omrani

2017

Numerical Methods Partial

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In this article, some high‐order accurate difference schemes of dispersive shallow water waves with Rosenau‐KdV‐RLW‐equation are presented. The corresponding conservative quantities are discussed. Existence of the numerical solution has been shown. A priori estimates, convergence, uniqueness, and stability of the difference schemes are proved. The convergence order is O ( h 4 + k 2 ) in the uniform norm without any restrictions on the mesh sizes. At last numerical results are given to support the theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves

Ghiloufi

Omrani

2017

Numerical Methods Partial

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“…Till now, the classical solution and the distributive solution to IBVP of (1.2) have been shown to uniquely exist in [2,3]. However, IBVP (1.1) has only been proved to admit a unique classical solution ( see [7,8]), although many works have been done from a numerical point of view ( see [4]- [6], for example). Yet, it is still an unsolved problem that whether IBVP (1.1) admits a distributional solution as u 0 ∈ H s (0, 1) with 0 ≤ s < 4.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous initial–boundary value problem of the Rosenau equation posed on a finite interval

Zhou

2016

Applied Mathematics Letters

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This paper considers the IBVP of the Rosenau equation      ∂ t u + ∂ t ∂ 4 x u + ∂ x u + u∂ x u = 0, x ∈ (0, 1), t > 0, u(0, x) = u 0 (x) u(0, t) = ∂ 2 x u(0, t) = 0, u(1, t) = ∂ 2 x u(1, t) = 0. It is proved that this IBVP has a unique global distributional solution u ∈ C([0, T ]; H s (0, 1)) as initial data u 0 ∈ H s (0, 1) with s ∈ [0, 4]. This is a new global well-posedness result on IBVP of the Rosenau equation with Dirichlet boundary conditions.

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Concircular Curvature Tensor’s Properties on Lorentzian Para-Sasakian Manifolds

Pandey

Prasad

Verma

2020

Springer Proceedings in Mathematics &Amp; Statistics

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The convergence of fully discrete Galerkin approximations of the Rosenau equation

Cited by 15 publications

References 2 publications

New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves

New conservative difference schemes with fourth‐order accuracy for some model equation for nonlinear dispersive waves

Homogeneous initial–boundary value problem of the Rosenau equation posed on a finite interval

Concircular Curvature Tensor’s Properties on Lorentzian Para-Sasakian Manifolds

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