Initial Value Problem
المؤلف:
Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C
المصدر:
Computational Differential Equations. Lund, Sweden: Studentlitteratur, 1996.
الجزء والصفحة:
...
13-6-2018
5130
Initial Value Problem
An initial value problem is a problem that has its conditions specified at some time 
. Usually, the problem is an ordinary differential equation or a partial differential equation. For example,
![<span style=]() {(partial^2u)/(partialt^2)-del ^2u=f in Omega; u=u_0 t=t_0; u=u_1 on partialOmega, " src="http://mathworld.wolfram.com/images/equations/InitialValueProblem/NumberedEquation1.gif" style="height:88px; width:155px" /> |
(1)
|
where 
denotes the boundary of 
, is an initial value problem.
REFERENCES:
Eriksson, K.; Estep, D.; Hansbo, P.; and Johnson, C. Computational Differential Equations. Lund, Sweden: Studentlitteratur, 1996.
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Initial Value Problems." Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, p. 829, 1992.
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