Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution

Kumar, Manoj; Singh, Neelima

doi:10.1016/j.camwa.2012.05.003

Cited by 4 publications

(4 citation statements)

References 21 publications

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“…• TFIRKT6: Three-stage sixth-order explicit improved TDRKT method with trigonometrically-fitting technique. • EFTDRKT6: Exponentially-fitted explicit TDRKT method with three stages sixthorder, the exponential technique is implemented into the method constructed by (Kumar & Singh, 2012). According to Duffy and Wilson (1997), thin film flow can describe the dynamic balance between surface tension and viscous force in the thin film layer without gravity.…”

Section: Resultsmentioning

confidence: 99%

Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third-Order IVPs

Chien¹,

Senu²,

Ahmadian³

et al. 2023

JST

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This study aims to propose sixth-order two-derivative improved Runge-Kutta type methods adopted with exponentially-fitting and trigonometrically-fitting techniques for integrating a special type of third-order ordinary differential equation in the form u^''' (t)=f(t,u(t),u^' (t)). The procedure of constructing order conditions comprised of a few previous steps, k-i for third-order two-derivative Runge-Kutta-type methods, has been outlined. These methods are developed through the idea of integrating initial value problems exactly with a numerical solution in the form of linear composition of the set functions e^ѡt and e^(-ѡt)for exponentially fitted and e^iѡt and e^(-iѡt) for trigonometrically-fitted with ѡ ϵ R. Parameters of two-derivative Runge-Kutta type method are adapted into principle frequency of exponential and oscillatory problems to construct the proposed methods. Error analysis of proposed methods is analysed, and the computational efficiency of proposed methods is demonstrated in numerical experiments compared to other existing numerical methods for integrating third-order ordinary differential equations with an exponential and periodic solution.

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Section: Resultsmentioning

confidence: 99%

Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third-Order IVPs

Chien¹,

Senu²,

Ahmadian³

et al. 2023

JST

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“…. This part is primarily concerned with the Cauchy problem for the doubly degenerate equation (3). King [9] gave the solution of (3) in the form:…”

Section: Exact Traveling Wave Solution Of the Second Generalization Omentioning

confidence: 99%

“…which in general has important applications in geology, biophysics, physics, and engineering (see [1][2][3]). Also known as the lubrication equation [4], it models the spreading motion of the free surface of a thin film on a solid substrate [5].…”

Section: Introductionmentioning

confidence: 99%

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New Application of the(G′/G)-Expansion Method for Thin Film Equations

Taha

Noorani

Hashim

2013

Abstract and Applied Analysis

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The(G′/G)-expansion method is used for the first time to find traveling wave solutions for thin film equations, where it is found that the related balance numbers are not the usual positive integers. The closed-form solution obtained via this method is in good agreement with the previously obtained solutions of other researchers. It is also noted that, for appropriate parameters, new solitary waves solutions are found.

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High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems

et al. 2021

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Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution

Cited by 4 publications

References 21 publications

Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third-Order IVPs

Efficient Frequency-Dependent Coefficients of Explicit Improved Two-Derivative Runge-Kutta Type Methods for Solving Third-Order IVPs

New Application of the(G′/G)-Expansion Method for Thin Film Equations

High-order exponentially fitted and trigonometrically fitted explicit two-derivative Runge–Kutta-type methods for solving third-order oscillatory problems

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