Unified matrix presentation of Maxwell's and wave equations using generalized differential matrix operators [EM engineering education]

1998 ◽  
Vol 41 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Yinchao Chen ◽  
Kunquan Sun ◽  
B. Beker ◽  
R. Mittra
Keyword(s):  
Engineering Education ◽  
Wave Equations ◽  
Generalized Differential ◽  
Matrix Operators ◽  
Differential Matrix

Calculation of the Natural Frequencies of Transverse Vibration of Complex Beams Using the Differential-Matrix Equations

2011 ◽  
Vol 243-249 ◽  
pp. 284-289
Author(s):  
Yu Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Composite Beams ◽  
Matrix Equations ◽  
Generalized Differential ◽  
Set Up ◽  
Differential Matrix

The generalized differential-matrix equations of transverse vibration of the beams were set up and they were solved by means of Cauchy sequence iterative method. Then according to the boundary conditions at two ends of the beams the natural frequencies of the transverse vibration of the different beams including the complex beams of non-uniform section and composite beams under different boundary conditions were figured out. The form of the differential-matrix is simple. The calculation of the sequence iterations can be accomplished by simple computer program. Using the method in this paper, the amount of work of calculation is reduced greatly and the results are accurate compared with the approximate method in which a beam of non-uniform section is replaced by many small segments of equal cross-section.

Solving the Linear Time-Fractional Wave Equation by Generalized Differential Transform Method

2012 ◽  
Vol 204-208 ◽  
pp. 4476-4480 ◽  
Author(s):  
Xue Hui Chen ◽  
Liang Wei ◽  
Ji Zhe Sui ◽  
Lian Cun Zheng
Keyword(s):  
Wave Equations ◽  
Linear Time ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Wave Equations ◽  
Generalized Differential ◽  
Time Fractional Wave Equation ◽  
Generalized Taylor’S Formula

In this paper, the generalized differential transform method is implemented for solving time-fractional wave equations in fluid mechanics. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor’s formula. The results reveal the method is feasible and convenient for handling approximate solutions of time-fractional partial differential equations.

scholarly journals Analyticity of Semigroups Generated by Singular Differential Matrix Operators

2010 ◽  
Vol 01 (04) ◽  
pp. 283-287
Author(s):  
Ould Ahmed Mahmoud Sid Ahmed ◽  
Adel Saddi
Keyword(s):  
Matrix Operators ◽  
Differential Matrix

scholarly journals Analytical solutions of generalized differential equations using quadratic-phase Fourier transform

2021 ◽  
Vol 7 (2) ◽  
pp. 1925-1940
Author(s):  
Firdous A. Shah ◽  
◽  
Waseem Z. Lone ◽  
Kottakkaran Sooppy Nisar ◽  
Amany Salah Khalifa ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Wave Equations ◽  
Preliminary Results ◽  
Quadratic Phase ◽  
Generalized Differential

<abstract><p>The aim of this study is to obtain the analytical solutions of some prominent differential equations including the generalized Laplace, heat and wave equations by using the quadratic-phase Fourier transform. To facilitate the narrative, we formulate the preliminary results vis-a-vis the differentiation properties of the quadratic-phase Fourier transform. The obtained results are reinforced with illustrative examples.</p></abstract>

A Unique Departure in Engineering Education

1899 ◽  
Vol 48 (1248supp) ◽  
pp. 19999-20000
Author(s):  
Edward Orton
Keyword(s):  
Engineering Education
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