Fast Computing Approaches Based on a Bilinear Pseudo-Spectral Method for Nonlinear Acoustic Wave Equations

Khasi, M.; Rashidinia, Jalil; Rasoulizadeh, Mohammad Navaz

doi:10.1137/22m1506390

Cited by 3 publications

(1 citation statement)

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“…Nonlinear partial differential equations (NPDEs) govern many natural phenomena arising in mathematical physics and engineering sciences [13][14][15]. Nonlinear waves are an important scientific research field.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

AL-saedi,

Nikan,

Avazzadeh

et al. 2023

Symmetry

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This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.

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Section: Introductionmentioning

confidence: 99%