Relevant bibliographies by topics / Time-dependent diffusion equation, Differential quadrature method, Runge-Kutta method

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  1. Journal articles
  2. Dissertations / Theses

Academic literature on the topic 'Time-dependent diffusion equation, Differential quadrature method, Runge-Kutta method'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Time-dependent diffusion equation, Differential quadrature method, Runge-Kutta method"

1

Gurarslan, Gurhan. "Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters." Mathematics 9, no. 9 (2021): 1027. http://dx.doi.org/10.3390/math9091027.

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A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge–Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by t
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2

Chen, Ling, You-Qi Tang, Shuang Liu, Yuan Zhou, and Xing-Guang Liu. "Nonlinear Phenomena in Axially Moving Beams with Speed-Dependent Tension and Tension-Dependent Speed." International Journal of Bifurcation and Chaos 31, no. 03 (2021): 2150037. http://dx.doi.org/10.1142/s0218127421500371.

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This paper investigates some nonlinear dynamical behaviors about domains of attraction, bifurcations, and chaos in an axially accelerating viscoelastic beam under a time-dependent tension and a time-dependent speed. The axial speed and the axial tension are coupled to each other on the basis of a harmonic variation over constant initial values. The transverse motion of the moving beam is governed by nonlinear integro-partial-differential equations with the rheological model of the Kelvin–Voigt energy dissipation mechanism, in which the material derivative is applied to the viscoelastic constit
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3

DING, HU, and JEAN W. ZU. "PERIODIC AND CHAOTIC RESPONSES OF AN AXIALLY ACCELERATING VISCOELASTIC BEAM UNDER TWO-FREQUENCY EXCITATIONS." International Journal of Applied Mechanics 05, no. 02 (2013): 1350019. http://dx.doi.org/10.1142/s1758825113500191.

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This study focuses on the steady-state periodic response and the chaotic behavior in the transverse motion of an axially moving viscoelastic tensioned beam with two-frequency excitations. The two-frequency excitations come from the external harmonic excitation and the parametric excitation from harmonic fluctuations of the moving speed. A dynamic model is established to include the finite axial support rigidity, the material derivative in the viscoelastic constitution relation, and the longitudinally varying tension due to the axial acceleration. The derived nonlinear integro-partial-different
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4

Mittal, Ramesh Chand, Sudhir Kumar, and Ram Jiwari. "A cubic B-spline quasi-interpolation method for solving two-dimensional unsteady advection diffusion equations." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 9 (2020): 4281–306. http://dx.doi.org/10.1108/hff-07-2019-0597.

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Purpose The purpose of this study is to extend the cubic B-spline quasi-interpolation (CBSQI) method via Kronecker product for solving 2D unsteady advection-diffusion equation. The CBSQI method has been used for solving 1D problems in literature so far. This study seeks to use the idea of a Kronecker product to extend the method for 2D problems. Design/methodology/approach In this work, a CBSQI is used to approximate the spatial partial derivatives of the dependent variable. The idea of the Kronecker product is used to extend the method for 2D problems. This produces the system of ordinary dif
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Dissertations / Theses on the topic "Time-dependent diffusion equation, Differential quadrature method, Runge-Kutta method"

1

Akman, Makbule. "Differential Quadrature Method For Time-dependent Diffusion Equation." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1224559/index.pdf.

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This thesis presents the Differential Quadrature Method (DQM) for solving time-dependent or heat conduction problem. DQM discretizes the space derivatives giving a system of ordinary differential equations with respect to time and the fourth order Runge Kutta Method (RKM) is employed for solving this system. Stabilities of the ordinary differential equations system and RKM are considered and step sizes are arranged accordingly. The procedure is applied to several time dependent diffusion problems and the solutions are presented in terms of graphics comparing with the exact solutions. Thi
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