Addendum: Quantitative Estimates for a Nonlinear System of Integrodifferential Equations Arising in Reactor Dynamics

1974 ◽  
Vol 5 (2) ◽  
pp. 349-349 ◽  
Author(s):  
J. A. Nohel
Keyword(s):  
Nonlinear System ◽  
Integrodifferential Equations ◽  
Reactor Dynamics ◽  
Quantitative Estimates ◽  
System Of Integrodifferential Equations

scholarly journals Application of Rational Second Kind Chebyshev Functions for System of Integrodifferential Equations on Semi-Infinite Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Tavassoli Kajani ◽  
S. Vahdati ◽  
Zulkifly Abbas ◽  
Mohammad Maleki
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Galerkin Method ◽  
High Accuracy ◽  
Integrodifferential Equations ◽  
Expansion Test ◽  
Infinite Intervals ◽  
System Of Integrodifferential Equations ◽  
Rational Chebyshev ◽  
Chebyshev Functions

Rational Chebyshev bases and Galerkin method are used to obtain the approximate solution of a system of high-order integro-differential equations on the interval [0,∞). This method is based on replacement of the unknown functions by their truncated series of rational Chebyshev expansion. Test examples are considered to show the high accuracy, simplicity, and efficiency of this method.

The Pressure and Film Thickness Distributions in Point Elastohydrodynamic Contact Under Dynamic Load

2005 ◽  
Author(s):  
M. Ya. Panovko
Keyword(s):  
Steady State ◽  
Nonlinear System ◽  
Free Boundary ◽  
Film Thickness ◽  
Newton Method ◽  
Dynamic Load ◽  
Mathematical Formulation ◽  
Point Contact ◽  
System Of Equations ◽  
System Of Integrodifferential Equations

Isothermal elastohydrodynamic (EHD) problem for dynamically loaded lubricated point contact is formulated and studied numerically. Mathematical formulation is based on the time depending nonlinear system of integrodifferential equations. In order to determine the location of the exit (free) boundary the problem is formulated as a problem of complementarity. The dimensionless system of equations and inequalities is solved using Newton method. Peculiarities of the influence of non-steady state (sinusoidal) loading on pressure and film thickness in the point EHD contact are shown.

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