A Collocation Method for the Numerical Solution of Laplace’s Equation with Nonlinear Boundary Conditions on a Polygon

1993 ◽  
Vol 30 (3) ◽  
pp. 717-732 ◽  
Author(s):  
Robert L. Doucette
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Laplace’S Equation ◽  
Laplace's Equation

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.

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