scholarly journals Numerical solution of fractional-order Riccati differential equation by differential quadrature method based on Chebyshev polynomials

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Jianhua Hou ◽  
Changqing Yang
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Riccati Differential Equation

Differential Quadrature Method in Computational Mechanics: A Review

1996 ◽  
Vol 49 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Charles W. Bert ◽  
Moinuddin Malik
Keyword(s):  
Numerical Solution ◽  
Computational Mechanics ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Solution Technique ◽  
General Interest ◽  
Quadrature Method ◽  
Physical Sciences ◽  
Boundary Problems ◽  
Potential Alternative

The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

scholarly journals Differential Quadrature Solution of Hyperbolic Telegraph Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
B. Pekmen ◽  
M. Tezer-Sezgin
Keyword(s):  
Numerical Solution ◽  
Good Accuracy ◽  
Differential Quadrature Method ◽  
Telegraph Equation ◽  
Differential Quadrature ◽  
Time Interval ◽  
Quadrature Method ◽  
Time Level ◽  
Time Direction ◽  
Grid Points

Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.

scholarly journals Dynamic Analysis of Electrostatic Microactuators Using the Differential Quadrature Method

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Ming-Hung Hsu
Keyword(s):  
Differential Equation ◽  
Dynamic Behavior ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Electrostatic Actuator ◽  
Discrete Eigenvalue ◽  
Electrostatic Actuators ◽  
Finite Element Package ◽  
Length Width

This work studies the dynamic behavior of electrostatic actuators using finite-element package software (FEMLAB) and differential quadrature method. The differential quadrature technique is used to transform partial differential equations into a discrete eigenvalue problem. Numerical results indicate that length, width, and thickness significantly impact the frequencies of the electrostatic actuators. The thickness could not affect markedly the electrostatic actuator capacities. The effects of varying actuator length, width, and thickness on the dynamic behavior and actuator capacities in electrostatic actuator systems are investigated. The differential quadrature method is an efficient differential equation solver.

Free vibration analysis of a rotating double tapered beam with flexible root via differential quadrature method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Tolga Tolga Yavuz ◽  
İbrahim Özkol
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Operating Conditions ◽  
Design Parameters ◽  
Quadrature Method ◽  
Content Type ◽  
Uniform Beam ◽  
Governing Differential Equation

Purpose This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters. Design/methodology/approach Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time. Findings The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions. Originality/value The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

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