Finite Difference Approximate Solutions for

Chung, S. K.

doi:10.1080/00036819808840652

Cited by 56 publications

(20 citation statements)

References 4 publications

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“…Besides the theoretical analysis, numerical studies of Eq. (3) also exist in the literature, see [22][23][24][25][26] and references therein. By adding the term −u x xt into the Rosenau equation, one can obtain the following Rosenau-RLW equation [27][28][29][30][31]:…”

Section: Introductionmentioning

confidence: 94%

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

2015

Nonlinear Dyn

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Recently, Biswas et al. (Phys Wave Phenom 19:24-29, 2011) derived exact bright and dark solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity, and Hu et al. (Adv Math Phys 11, Article ID 217393, 2014) proposed two conservative finite difference schemes for the usual RosenauKawahara equation. In this paper, we obtain another set of exact solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity. More importantly, a conservative finite difference method is presented. The fundamental energy conservation law is preserved by the current numerical scheme. And the existence and uniqueness of the numerical solution are proved. The convergence and stability of the numerical solution are also shown. The method is second-order convergent both in time and in space. Finally, numerical results confirm well with the theoretical results and show that the current method can be well used to study the solitary wave at long time.

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Section: Introductionmentioning

confidence: 94%

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

2015

Nonlinear Dyn

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“…Park [3] presented results about existence and uniqueness of the solutions to Equation (7). In the context of the Rosenau equation, many numerical methods based on the Faedo-Galerkin method, finite element Galerkin methods, finite difference methods, orthogonal cubic spline collocation methods have been employed [4][5][6][7][8][9]. Manickam et al [10] employed the second-order splitting method to approximate the solutions of the Rosenau equation.…”

Section: Abstract Convergence Analysis Operator Splitting Rosenau-bmentioning

confidence: 99%

On the convergence of operator splitting for the Rosenau–Burgers equation

Zürnacı

Seydaoğlu

2019

Numerical Methods Partial

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We present convergence analysis of operator splitting methods applied to the nonlinear Rosenau-Burgers equation. The equation is first splitted into an unbounded linear part and a bounded nonlinear part and then operator splitting methods of Lie-Trotter and Strang type are applied to the equation. The local error bounds are obtained by using an approach based on the differential theory of operators in Banach space and error terms of one and two-dimensional numerical quadratures via Lie commutator bounds. The global error estimates are obtained via a Lady Windermere's fan argument. Lastly, a numerical example is studied to confirm the expected convergence order.

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“…(2), many studies have been performed by the scholars. [17][18][19][20][21][22] Then, for the other consideration of the nonlinear wave, Jin-Ming Zuo developed the following so-called Rosenau-KdV equation and discussed the solitary wave solutions and periodic solutions of the equation with the sine-cosine and the tanh methods in Ref. [23].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Dispersive Shallow Water Waves with an Efficient Method

Karakoç

Biswas

2015

j comput theor nanosci

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The main purpose of this paper has been to compare the numerical results when the septic B-spline is used in the collocation method, and performance of the splitting technique in the numerical methods has been investigated. So numerical solutions of the Rosenau-KdV equation have been constructed by using the collocation method with septic B-splines as interpolation functions. The Rosenau-KdV equation is split both in space and in time. Those coupled systems of differential equations are also solved by way of the septic B-spline collocation method over uniform finite intervals.

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Finite Difference Approximate Solutions for

Cited by 56 publications

References 4 publications

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

On the convergence of operator splitting for the Rosenau–Burgers equation

Numerical Simulation of Dispersive Shallow Water Waves with an Efficient Method

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