Simulations of solitary waves of RLW equation by exponential B-spline Galerkin method

Görgülü, Melis Zorşahin; Dağ, İdris; Irk, Dursun

doi:10.1088/1674-1056/26/8/080202

Cited by 16 publications

(2 citation statements)

References 31 publications

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“…where 4) becomes the RLW equation [44,45]: f 4 (t) = 0.01 cos(0.5t), c 1 = c 2 = c 4 = 1, for α = 0.25, 0.5, 1, Fig. 6 gives wave motions of the white noise functional solution of (73).…”

Section: Discussionmentioning

confidence: 99%

Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

Kim

Sakthivel

Debbouche

et al. 2020

Chaos, Solitons & Fractals

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In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schrödinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an improved computational method. Specifically, the Hermite transform is employed for transforming Wick-type stochastic nonlinear partial differential equations into deterministic nonlinear partial differential equations with integral and fraction order. Furthermore, the required set of stochastic solutions in the white noise space is obtained by using the inverse Hermite transform. Based on the derived solutions, the dynamics of the considered equations are performed with some particular values of the physical parameters. The results reveal that the proposed improved computational technique can be applied to solve various kinds of Wick-type stochastic fractional partial differential equations.

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“…where 4) becomes the RLW equation [44,45]: f 4 (t) = 0.01 cos(0.5t), c 1 = c 2 = c 4 = 1, for α = 0.25, 0.5, 1, Fig. 6 gives wave motions of the white noise functional solution of (73).…”

Section: Discussionmentioning

confidence: 99%

Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

Kim

Sakthivel

Debbouche

et al. 2020

Chaos, Solitons & Fractals

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“…Example 2. In this second example (given in [27]), we will consider the interaction between two waves with two different amplitudes moving in the same direction. Te initial , where for all j � 1, 2, we have…”

Section: Illustration Of Numerical Performancementioning

confidence: 99%

A Higher‐Order Improved Runge–Kutta Method and Cubic B‐Spline Approximation for the One‐Dimensional Nonlinear RLW Equation

Redouane

Arar

Makhlouf

et al. 2023

Mathematical Problems in Engineering

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This article developed a significant improvement of a Galerkin-type approximation to the regularized long-wave equation (RLW) solution under homogeneous Dirichlet boundary conditions for achieving higher accuracy in time variables. First, a basis derived from cubic B-splines and limit conditions is used to perform a Galerkin-type approximation. Then, a Crank–Nicolson and fourth-order 4-stage improved Runge–Kutta scheme (IRK4) is used to discretize time. Both a strong stability analysis of a fully discrete IRK4 scheme and the evaluation of Von Neumann stability of the proposed Crank–Nicolson technique are examined. We demonstrate the efficiency of our method with two test problems. The analytical and numerical solutions found in the literature are then contrasted with the approximate solutions produced by the suggested method. The validated numerical results illustrate that the provided technique is more efficient and converges faster than earlier research, resulting in less computational time, smaller space dimensions, and storage. As a result, the proposed numerical approach is appealing for approximating PDEs whose explicit solution is unknown for a variety of boundary conditions.

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Numerical Investigations of Physical Processes for Regularized Long Wave Equation

Hepson

Yiğit

2021

Advances in Intelligent Systems and Computing

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Simulations of solitary waves of RLW equation by exponential B-spline Galerkin method

Cited by 16 publications

References 31 publications

Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

A Higher‐Order Improved Runge–Kutta Method and Cubic B‐Spline Approximation for the One‐Dimensional Nonlinear RLW Equation

Numerical Investigations of Physical Processes for Regularized Long Wave Equation

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