Complex solutions to the higher-order nonlinear boussinesq type wave equation transform

Kılıç, Sıdıka Şule Şener; Çelık, Ercan

doi:10.1007/s11587-022-00698-1

Cited by 7 publications

(2 citation statements)

References 39 publications

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“…Model Equation (1) has numerous applications in physics, mathematics, and engineering (Liu et al [1]. According to Kamran et al [2], it can be used to describe many real-life physical systems, among which are the Langmuir wave packet estimation in plasma, electrostatics, the non-relativistic limit of the Klein-Gordon equation, fluid flow, and bimolecular dynamics (Kilic and Celik [3], Akbarov et al [4], Chen et al [5], Singh et al [6], Mirzaee et al [7], Khan et al [8], and Aliev et al [9]). These classes of partial differential equations lack analytic solutions and are very difficult to approximate due to the nonlinear parameters.…”

Section: Introductionmentioning

confidence: 99%

Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies

Omole,

Adeyefa,

Ayodele

et al. 2023

Axioms

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A computational approach with the aid of the Linear Multistep Method (LMM) for the numerical solution of differential equations with initial value problems or boundary conditions has appeared several times in the literature due to its good accuracy and stability properties. The major objective of this article is to extend a multistep approach for the numerical solution of the Partial Differential Equation (PDE) originating from fluid mechanics in a two-dimensional space with initial and boundary conditions, as a result of the importance and utility of the models of partial differential equations in applications, particularly in physical phenomena, such as in convection-diffusion models, and fluid flow problems. Thus, a multistep collocation formula, which is based on orthogonal polynomials is proposed. Ninth-order Multistep Collocation Formulas (NMCFs) were formulated through the principle of interpolation and collocation processes. The theoretical analysis of the NMCFs reveals that they have algebraic order nine, are zero-stable, consistent, and, thus, convergent. The implementation strategies of the NMCFs are comprehensively discussed. Some numerical test problems were presented to evaluate the efficacy and applicability of the proposed formulas. Comparisons with other methods were also presented to demonstrate the new formulas’ productivity. Finally, figures were presented to illustrate the behavior of the numerical examples.

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Section: Introductionmentioning

confidence: 99%

Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies

Omole,

Adeyefa,

Ayodele

et al. 2023

Axioms

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“…Nonlinearity arises by both finite stress values and elastic material properties whereas the dispersion arises the finite transverse dimension of the rod in the process that is expressed by a Boussinesq-type equation or double dispersion equation (Porubov and Velarde, 2000; Samsonov et al. , 1994; Kiliç and Çelik, 2022).…”

Section: Introductionmentioning

confidence: 99%

The solutions of dissipation-dispersive models arising in material science

Pınar

2022

MMMS

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PurposeThe aim of this work is to obtain periodic waves of Eq. (1) via ansatz-based methods. So, the open questions are replied and the gap will be filled in the literature. Additionally, the comparison of the considered models (Eq. (1) and Eq. (2)) due to their performance. Although it is extremely difficult to find the exact wave solutions in Eq. (1) and Eq. (2) without any assumptions, the targeted solutions have been obtained with the chosen method.Design/methodology/approachMaterial science is the today's popular research area. So, the well-known model is the dissipation double dispersive nonlinear equation and, in the literature, open queries have been seen. The aim of this work is to reply open queries by obtaining wave solutions of the dissipation double dispersive model, double dispersive model and double dispersive model for Murnaghan's material via ansatz-based methods.FindingsThe results have been appeared for the first time in this communication work and they may be valuable for developing uses in material science.Originality/valueThe exact wave solutions of Eq. (1) and Eq. (2) without any assumptions have been obtained with via ansatz-based method. So, the open questions are replied and the gap will be filled in the literature.

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A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

et al. 2023

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Complex solutions to the higher-order nonlinear boussinesq type wave equation transform

Cited by 7 publications

References 39 publications

Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies

Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies

The solutions of dissipation-dispersive models arising in material science

A study of propagation of the ultra-short femtosecond pulses in an optical fiber by using the extended generalized Riccati equation mapping method

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