A robust semi-explicit difference scheme for the Kuramoto–Tsuzuki equation

Wang, Ting-Chun; Guo, Boling

doi:10.1016/j.cam.2009.07.058

Cited by 26 publications

(10 citation statements)

References 5 publications

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“…For some different values of and ℎ, we list errors of Scheme I and Scheme II at several different time in Tables 1 and 2, respectively. We verify the two-order accuracy of the difference scheme in Tables 3 and 4 by using the method of [26,27]. The numerical simulation of two conservative quantities (6) and 7is listed in Tables 5 and 6.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

et al. 2014

Advances in Mathematical Physics

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Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

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Section: Numerical Simulationsmentioning

confidence: 99%

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

et al. 2014

Advances in Mathematical Physics

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“…It is easy to see that the calculation results of scheme I are slightly better than scheme II. Using the method in [20,21], we verified the second convergence of the difference scheme in Table 3. Numerical simulations on the conservation invariant are given in Table 4.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Conservative Difference Scheme for Generalized Rosenau-KdV Equation

Luo

Feng

2014

Advances in Mathematical Physics

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“…the finite difference method with the explicit and symmetrical Euler integration in time [20,21,26,27] and the pseudospectral method [29]. A mixture of implicit and semi-explicit integration techniques are used in [3,28]. The stability analysis is done in the specified energy norms and uniform error estimates are proved by using embedding theorems.…”

Section: Introductionmentioning

confidence: 99%

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

Leonavičienė

Bugajev

Jankevičiūtė

et al. 2016

Mathematical Modelling and Analysis

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Abstract. A general methodology for the stability analysis of discrete approximations of nonstationary PDEs is applied to solve the Kuramoto-Tsuzuki equation, including also the Schrödinger problem. Stability regions are constructed for the explicit, backward and symmetrical Euler schemes. The obtained results are applied to solve the Kuramoto-Tsuzuki problem with a non-local integral boundary condition. Results of computational experiments are provided.

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A robust semi-explicit difference scheme for the Kuramoto–Tsuzuki equation

Cited by 26 publications

References 5 publications

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

Two Conservative Difference Schemes for Rosenau-Kawahara Equation

Conservative Difference Scheme for Generalized Rosenau-KdV Equation

On Stability Analysis of Finite Difference Schemes for Generalized Kuramoto-Tsuzuki Equation With Nonlocal Boundary Conditions

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