A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation

Wang, Xuping; Sun, Zhi‐zhong

doi:10.1002/num.22646

Cited by 8 publications

(3 citation statements)

References 37 publications

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“…In the early years, two layers of numerical solution from consecutive time steps are involved in the schemes. See [26][27][28][29][30] for examples. It is also common to use three layers of numerical solutions.…”

Section: Analytic Propertymentioning

confidence: 99%

An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

2021

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We formulate and analyze a new finite difference scheme for a shallow water model in the form of viscous Burgers-Poisson system with periodic boundary conditions. The proposed scheme belongs to a family of three-level linearized finite difference methods. It is proved to preserve both momentum and energy in the discrete sense. In addition, we proved that the method converges uniformly and has second order of accuracy in space. The analysis given in this work is the first time a pointwise error estimation is done on a second-order finite difference operator applied to the Burgers-Poisson system. We validate our findings by performing various numerical simulations on both viscous and inviscous problems. These numerical examples show the efficacy of the proposed method and confirm the proven theoretical results.

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Section: Analytic Propertymentioning

confidence: 99%

An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

2021

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“…Soon afterwards, employing the nonuniform L2-1 σ method to approximate Caputo time-fractional derivative, Cen et al [24] established a high-order difference scheme for the time-fractional KdV-Burgers equation with initial singularity, which was analyzed unconditional stable and min{rα, 2}-th order temporal convergence and first-order spatial convergence by the energy method. In the same year, Wang and Sun [25] presented a two-level implicit difference scheme for the KdV equation by the method of order reduction, which had the second order convergence rate both in space and time. For the ZK equation, Nishiyama et al [26] developed a conservative finite difference scheme for the gZK equation by the discrete variational method and proved the conservation of mass and energy.…”

Section: Introductionmentioning

confidence: 99%

A second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation

Chen,

Wang

2024

Preprint

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In this paper, we investigate the numerical method for the two dimensional time-fractional Zakharov-Kuznetsov equation. By the method of order reduction, the model is first transformed to an equivalent system. A nonlinear difference scheme is then proposed to solve the equivalent model, with min{2, rα}-th order accuracy in time and second-order accuracy in space, where α ∈ (0, 1) is the fractional order and the grading parameter r ≥ 1. The existence of the numerical solution is carefully studied by the renowned Browder fixed point theorem. With the aid of Grönwall inequality and some crucial skills, we analyze the unconditional stability and convergence of the proposed scheme based on the energy method. Finally, numerical experiments are given to illustrate the correctness of our theoretical analysis. 2010 MSC: 65M06, 65M12, 35R11

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“…Method of generalized differential quadrature algorithm for and with several effects are discussed by Ashraf et al 77 Different techniques of converting the PDEs into ordinary differential equations (ODEs) and the numerical solution is made with similarity transformations by several investigators. 78,79 The prime objective of the current review is to get an overview of synthesizing ordinary nanofluid and hybrid nanofluid with magnetic field and thermal radiation and also state the previous research work in the nanofluid and numeric solution of PDEs. All mentioned studies became an inspiration for this effort that different fluids with different nanoparticles are exercised to obtain thermal properties, but a few scholars tried to discuss the hybrid nanofluid with the numerical solution of PDEs via different techniques.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme

et al. 2021

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Key developments in the field of nanotechnology have drawn the attention of many scholars toward the interaction of nanoparticles due to their capturing applications in solar energy systems and thermal engineering. Larger consumption of energy posed a challenge for thermal science, so thermal engineering is trying to solve this issue by increasing the thermal conductivity of the fluid. The thermal conductivity of conventional fluid is increased by incorporating the nanoparticles in the base fluid. Keeping this in mind, the present research project addresses the utilization of nanoparticles in a steady three-dimensional rotating flow of magnetohydrodynamic water-based hybrid fluid over an extending sheet. Nanoparticles of aluminum oxide (Al 2 O 3 ) and silver (Ag) are being used with water (H 2 O) as base fluid. The velocity of nanoparticles is being captured under the influence of an inclined magnetic field and the transport of heat is scrutinized through thermal radiation. The physical model generates partial differential equations and then transported into an equivalent set of a nonlinear ordinary differential equations. The purpose of numerical computation is made by the Lobatto IIIA method, which is

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A second order convergent difference scheme for the initial‐boundary value problem of Korteweg–de Vires equation

Cited by 8 publications

References 37 publications

An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

An Invariant-Preserving Scheme for the Viscous Burgers-Poisson System

A second-order scheme with nonuniform time grids for the two dimensional time-fractional Zakharov-Kuznetsov equation

Nanoscale energy transport of inclined magnetized 3D hybrid nanofluid with Lobatto IIIA scheme

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