Frequency Response of Fluid Lines With Nonlinear Boundary Conditions

1971 ◽  
Vol 93 (3) ◽  
pp. 365-372 ◽  
Author(s):  
R. D. Strunk
Keyword(s):  
Boundary Conditions ◽  
Perturbation Method ◽  
Numerical Solution ◽  
Frequency Response ◽  
Nonlinear Equations ◽  
Nonlinear Boundary ◽  
Harmonic Distortion ◽  
Nonlinear Boundary Conditions ◽  
Qualitative Information ◽  
Method Of Solution

The harmonic distortion generated when a fluid line is terminated by a nonlinear orifice characteristic is analyzed by using a perturbation method of solution. The perturbation method is shown to be representative of the true phenomenon and to give very good quantitative as well as qualitative information by comparing the results to a numerical solution of the nonlinear equations. The results presented describe the distortion phenomenon as a function of several dimensionless ratios.

A Fast New Algorithm for Solving a Nonlinear Beam Equation under Nonlinear Boundary Conditions

2017 ◽  
Vol 72 (5) ◽  
pp. 397-400 ◽  
Author(s):  
Chein-Shan Liu ◽  
Botong Li
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Nonlinear Boundary Conditions ◽  
Beam Equation ◽  
Test Functions ◽  
Nonlinear Beam ◽  
Expansion Coefficients ◽  
Sinusoidal Functions

AbstractFor the problem of a nonlinear beam equation under nonlinear boundary conditions of moments, a fast iterative method is developed by transforming the ordinary differential equation into an integral one. The sinusoidal functions are used subtly as test functions as well as the bases of numerical solution in the calculation. Due to the orthogonality of the sinusoidal functions, the expansion coefficients of numerical solution in closed form can be found easily. Hence, the iterative scheme converges very fast to find numerical solutions with high accuracy.

scholarly journals First order differential systems with a nonlinear boundary condition via the method of solution-regions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Marlène Frigon ◽  
Marcos Tella ◽  
F. Adrián F. Tojo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Boundary Conditions ◽  
Linear Case ◽  
Differential Systems ◽  
First Order ◽  
Method Of Solution

AbstractIn this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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