The corner solution for quasilinear differential equation with two parameters

1997 ◽  
Vol 18 (5) ◽  
pp. 503-510
Author(s):  
Zhang Hanlin
Keyword(s):  
Differential Equation ◽  
Quasilinear Differential Equation ◽  
Corner Solution ◽  
Two Parameters

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

A two parameter eigenvalue problem

1974 ◽  
Vol 10 (1) ◽  
pp. 39-50
Author(s):  
J.A. Rickard
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Order Differential Equation ◽  
Inviscid Fluid ◽  
Free Oscillations ◽  
Numerical Computations ◽  
Second Order Differential Equation ◽  
Independent Variable ◽  
Two Parameters ◽  
Two Parameter

An ordinary second order differential equation is considered in which the coefficients are dependent on two parameters ω and F as well as the independent variable μ. The equation arises in the study of free oscillations of incompressible inviscid fluid in global shells. An asymptotic technique is presented which estimates the eigenvaiues (that is the values of ω for which the solution is bounded for all |μ| ≤ 1) as functions of F, as F → ∞. The agreement of the results with numerical computations is also discussed.

The statistical distribution of the curvature of a random Gaussian surface

1958 ◽  
Vol 54 (4) ◽  
pp. 439-453 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Energy Spectrum ◽  
Third Order ◽  
The Third ◽  
Surface Slopes ◽  
Linear Differential ◽  
Two Parameters ◽  
Gaussian Surface ◽  
Special Case

ABSTRACTThe distribution of the total (or ‘second’) curvature of a stationary random Gaussian surface is derived on the assumption that the squares of the surface slopes are negligible. The distribution is found to depend on only two parameters, derivable from the fourth moments of the energy spectrum of the surface. Each distribution function satisfies a linear differential equation of the third order, and the distribution is asymmetrical with positive skewness, in general. A special case of zero skewness occurs when the surface consists of two intersecting systems of long-crested waves.

Method of Determining Damping and Elastic Properties of Rubber Used in Tires

1968 ◽  
Vol 41 (4) ◽  
pp. 943-952
Author(s):  
D. F. Moore ◽  
D. B. Larson
Keyword(s):  
Differential Equation ◽  
Elastic Properties ◽  
Nonlinear Differential Equation ◽  
Viscoelastic Behavior ◽  
Least Square ◽  
History Of ◽  
Dynamic Penetration ◽  
Voigt Model ◽  
Two Parameters ◽  
Tread Rubber

Abstract Dynamic penetration of tread rubber by asperities of a roadbed for a rolling tire was simulated by impact of a rubber specimen on different arrangements of small spheres. The penetration history of the draping rubber was then analyzed to determine its damping and elastic properties. The method of analysis essentially varied two parameters in a nonlinear differential equation that described the system, so as to minimize the error between the integrated equation and test data. Least square of minimization was used. The results indicated that the viscoelastic behavior of the rubber can be represented by a simple Voigt model. The importance of jointly considering both draping and traction zones in the contact patch of a rolling tire is discussed.

The Evaluation of Eigenvalues of a Differential Equation Arising in a Problem in Genetics

1962 ◽  
Vol 58 (4) ◽  
pp. 588-593 ◽  
Author(s):  
G. F. Miller ◽  
E. T. Goodwin
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Order Differential Equation ◽  
Finite Size ◽  
Second Order ◽  
Random Drift ◽  
Smallest Eigenvalue ◽  
Second Order Differential Equation ◽  
Two Parameters

ABSTRACTThis paper concerns the determination of the smallest eigenvalue of a second order differential equation containing two parameters which arises in problems concerning genic selection under random drift in a population of finite size. A table of values is given, the method of computation is described, and the asymptotic behaviour for large values of one of the parameters is investigated.

ON THE STRUCTURE OF THE SOLUTIONS OF A TWO-PARAMETER FAMILY OF THREE-DIMENSIONAL ORDINARY DIFFERENTIAL EQUATIONS

2003 ◽  
Vol 13 (05) ◽  
pp. 1287-1298 ◽  
Author(s):  
SERKAN T. IMPRAM ◽  
RUSSELL JOHNSON ◽  
RAFFAELLA PAVANI
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Wide Range ◽  
Two Parameters ◽  
Two Parameter ◽  
Autonomous Ordinary Differential Equation

We analyze the global structure of the solutions of a three-dimensional, autonomous ordinary differential equation which depends on two parameters. We use graphical, heuristic, and rigorous arguments to show that as the parameters vary, a wide range of dynamical behavior is displayed.

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