Shock wave solution of the variable coefficient nonlinear partial differential equations

Güner, Özkan

doi:10.1002/mma.3909

Cited by 6 publications

(2 citation statements)

References 37 publications

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“…A variable coefficient equation that generalizes equation (1) has the form which has been studied from different points of view. See, for example, in [12][13][14][15]. We assume that ( ) f t , ( ) g t and ( ) h t are nonzero smooth functions.…”

Section: Xy Y XX Xxxymentioning

confidence: 99%

Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation

Sophocleous

Tracinà

2018

Phys. Scr.

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We consider a general class of variable coefficient Calogero-Degasperis equations. The complete Lie group classification is performed with the aid of the appropriate equivalence group. Lie symmetries are used to derive a number of reductions by constructing the corresponding optimal lists of one-dimensional subalgebras of the Lie symmetry algebras. Furthermore, a number of non-Lie reductions are given. One of the reduced equations is the variable coefficient potential KdV equation which is studied from the point of view of Lie group analysis.

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Section: Xy Y XX Xxxymentioning

confidence: 99%

Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation

Sophocleous

Tracinà

2018

Phys. Scr.

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“…There are conditions, called as “shock conditions”, which decide the occurrence of shocks. These conditions can be used to find the state on the other side of the shock if a state on the one side of the shock is already known [ 4 , 50 ]. The results obtained from KFVS scheme are compared with the results of central NT scheme.…”

Section: Numerical Case Studiesmentioning

confidence: 99%

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

et al. 2018

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This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

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