Second-Order Evolution Equations and the Galerkin Method

1990 ◽  
pp. 919-957
Author(s):  
Eberhard Zeidler
Keyword(s):  
Galerkin Method ◽  
Evolution Equations ◽  
Second Order ◽  
The Galerkin Method

Galerkin method for optimal control of second-order evolution equations

2003 ◽  
Vol 27 (2) ◽  
pp. 221-230 ◽  
Author(s):  
Anna D??bińska-Nagórska ◽  
Andrzej Just ◽  
Zdzisaw Stempień
Keyword(s):  
Optimal Control ◽  
Galerkin Method ◽  
Evolution Equations ◽  
Second Order

scholarly journals Using the Galerkin method to compute the eigenvalues and eigenelements of the second-order Sturm–Liouville problems

2019 ◽  
Vol 163 (0) ◽  
pp. 27-42
Author(s):  
omar Mokhtar ◽  
wael Abbas ◽  
Mohamed Fathy ◽  
Ahmed A. M. Saidb, ◽  
Hesham ahmed mohammed abd-EL Gawad
Keyword(s):  
Galerkin Method ◽  
Second Order ◽  
Sturm Liouville ◽  
The Galerkin Method

Pole Placement for Delay Differential Equations with Time-Periodic Delays Using Galerkin Approximations (CND-20-1378)

2021 ◽  
Author(s):  
Shanti Swaroop Kandala ◽  
Thomas K. Uchida ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Delay Differential Equations ◽  
Second Order ◽  
Delay Systems ◽  
First Order ◽  
The Galerkin Method ◽  
Delay Differential ◽  
Time Periodic ◽  
Periodic Delays

Abstract Many practical systems have inherent time delays that cannot be ignored; thus, their dynamics are described using delay differential equations (DDEs). The Galerkin approximation method is one strategy for studying the stability of time-delay systems. In this work, we consider delays that are time-varying and, specifically, time-periodic. The Galerkin method can be used to obtain a system of ordinary differential equations (ODEs) from a second-order time-periodic DDE in two ways: either by converting the DDE into a second-order time-periodic partial differential equation (PDE) and then into a system of second-order ODEs, or by first expressing the original DDE as two first-order time-periodic DDEs, then converting into a system of first-order time-periodic PDEs, and finally converting into a first-order time-periodic ODE system. The difference between these two formulations in the context of control is presented in this paper. Specifically, we show that the former produces spurious Floquet multipliers at a spectral radius of 1. We also propose an optimization-based framework to obtain feedback gains that stabilize closed-loop control systems with time-periodic delays. The proposed optimization-based framework employs the Galerkin method and Floquet theory, and is shown to be capable of stabilizing systems considered in the literature. Finally, we present experimental validation of our theoretical results using a rotary inverted pendulum apparatus with inherent sensing delays as well as additional time-periodic state-feedback delays that are introduced deliberately.

Faedo-Galerkin method for nonlinear second-order evolution equations with Volterra operators

2007 ◽  
Vol 10 (2) ◽  
pp. 203-228 ◽  
Author(s):  
N. V. Zadoyanchuk ◽  
P. O. Kas’yanov
Keyword(s):  
Galerkin Method ◽  
Evolution Equations ◽  
Second Order ◽  
Volterra Operators

Non-Newtonian oscillatory layer flow, approximate solution

1979 ◽  
Vol 44 (10) ◽  
pp. 2908-2914 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Galerkin Method ◽  
Horizontal Plane ◽  
Oscillatory Flow ◽  
Oscillatory Boundary Layer ◽  
Layer Flow ◽  
Pseudoplastic Liquid ◽  
The Galerkin Method

The problem of the oscillatory flow of pseudoplastic liquid in vicinity of the infinitely long horizontal plane is formulated in stresses. For Re i.e. for conditions of oscillatory boundary layer the problem is solved approximately by the Galerkin method.

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