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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences


Author: Colin W. Cryer
Journal: Math. Comp. 25 (1971), 435-443
MSC: Primary 65N05
MathSciNet review: 0298961
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Abstract: A method for solving free boundary problems for journal bearings by means of finite differences has been proposed by Christopherson. We analyse Christopherson's method in detail for the case of an infinite journal bearing where the free boundary problem is as follows: Given $ T > 0$ and $ h(t)$ find $ \tau \in (0,T]$ and $ p(t)$ such that (i) $ [{h^3}p']' = h'$ for $ t \in (0,\tau )$, (ii) $ p(0) = 0$, (iii) $ p(t) = 0$ for $ t \in [\tau ,T]$, and (iv) $ p'(\tau - 0) = 0$.

First, it is shown that the discrete approximation is accurate to $ O({[\Delta t]^2})$ where $ \Delta t$ is the step size. Next, it is shown that the discrete problem is equivalent to a quadratic programming problem. Then, the iterative method for computing the discrete approximation is analysed. Finally, some numerical results are given.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1971-0298961-7
PII: S 0025-5718(1971)0298961-7
Keywords: Christopherson's method, free boundary problems, finite differences, journal bearings, quadratic programming, lubrication theory
Article copyright: © Copyright 1971 American Mathematical Society