 Ordinary differential equations: boundary value problemsIan Jacques and
Colin Judd
Chapter 8 in Numerical Analysis, 1987, pp 265-276 from Springer Abstract: Abstract Consider the second order differential equation 8.1 $$ y'' = f(x,y,y') $$ defined on an interval a ≤ x ≤ b. Here, f is a given function of three real variables and y is an unknown function of the independent variable x. The general solution of (8.1) contains two arbitrary constants, so in order to determine it uniquely it is necessary to impose two additional conditions on y. When one of these is given at x = a and the other at x = b, the problem is called a boundary value problem and the associated conditions are called boundary conditions. The simplest type of boundary conditions are 8.2a $$ y(a) = \alpha $$ 8.2b $$ y(b) = \beta $$ for given numbers α and β. However, more general conditions such as 8.3a $$ \lambda _1 y(a) + \lambda _2 y'(a) = \alpha _1 $$ 8.3b $$ \mu _1 y(b) + \mu _2 y'(b) = \alpha _2 $$ for given numbers λi, αi and ±i (i = 1,2) are sometimes imposed. Sufficient conditions for the existence and uniqueness of such problems may be found in Keller (1968). Date: 1987 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3157-2_8 Ordering information: This item can be ordered from DOI: 10.1007/978-94-009-3157-2_8 Access Statistics for this chapter More chapters in Springer Books from Springer |
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