Bounds for Initial Value Problems
Keyword(s):
A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type: x(¨t)+f(t,x,x)˙=0,x(0)=X0,x(˙0)=V0, where f is continuous with continuous first derivatives, Lipschitzian, and ∂f/∂x ≥ 0. An original bounding theorem has been formulated and proven and a numerical technique has been developed for finding the bounding functions in analytic form as linear combinations of Tchebyshev polynomials. The method has been applied to several problems of engineering interest.
1971 ◽
Vol 36
(2)
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pp. 283-300
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1995 ◽
Vol 05
(02)
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pp. 275-280
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2007 ◽
Vol 18
(03)
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pp. 419-431
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1993 ◽
Vol 441
(1912)
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pp. 283-289
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2005 ◽
Vol 461
(2058)
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pp. 1639-1658
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2013 ◽
Vol 58
◽
pp. 33-39
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1977 ◽
Vol 31
(140)
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pp. 922-922
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2009 ◽
Vol 20
(03)
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pp. 383-398
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