scholarly journals A parameterized non-intrusive reduced order model and error analysis for general time-dependent nonlinear partial differential equations and its applications

2017 ◽  
Vol 317 ◽  
pp. 868-889 ◽  
Author(s):  
D. Xiao ◽  
F. Fang ◽  
C.C. Pain ◽  
I.M. Navon
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Error Analysis ◽  
Nonlinear Partial Differential Equations ◽  
Reduced Order Model ◽  
Time Dependent ◽  
Order Model ◽  
Partial Differential ◽  
Reduced Order ◽  
General Time

scholarly journals The Fornberg-Whitham Equation Solved by the Differential Transform Method

2020 ◽  
pp. 85-95
Author(s):  
Helena Nayar ◽  
Patrick Azere Phiri
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Time Dependent ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Whitham Equation ◽  
Temporal Variable

The Differential Transform Method is a powerful analytical method that can solve nonlinear partial differential equations. Yet, the method cannot be used to solve time-dependent partial differential equations that involve more than one partial derivative with respect to the temporal variable t when they are of the same order, as in the case of the Fornberg-Whitham type equations. In this paper, a new theorem is devised to overcome the aforementioned problem ofthe method, and it has been successfully applied to solve the Fornberg-Whitham equation. The other equations belonging to this group of equations, such as the Camassa-Holm equation and the Degasperi-Procesi equation, may also be solved by this approach.

Reduced Order Model of Nanoelectromechanical Systems to Include Casimir Effect

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Roberto J. Zapata ◽  
Martin W. Knecht
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Second Order ◽  
Reduced Order Model ◽  
Order Partial Differential Equation ◽  
Order Model ◽  
Partial Differential ◽  
Reduced Order

This paper deals with electrostatically actuated nanoelectromechanical (NEMS) cantilever resonators. The dynamic behavior is described by a second order partial differential equation. The NEMS cantilever resonator device is actuatedby an AC voltage resulting in a vibrating motion of the cantilever. At nano scale, squeeze film damping, Casimir force, and fringing effects significantly influence the dynamic behavior or the cantilever beam. The second order partial differential equation is solved using the Reduced Order Model (ROM) method. The resulting time dependent second order differential equations system is then transformed into a first order differential equations system. Numerical simulations were conducted using Matlab solver ode15s.

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