Fredholm integro-differential equation |
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Authors: | G S Karkarashvili |
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Institution: | (1) Mathematical Institute, Georgian Academy of Sciences, USSR |
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Abstract: | We consider numerical solution of an integro-differential equation with nonsmooth initspaial values. Unique solvability in Sobolev spaceW
2
(0, 1), =1,2, is proved. We establish the rate of convergence of the approximate solution to the exact solution in fractional spacesW
2
+1
, 0![le](/content/q821308m37850502/xxlarge8804.gif) ![agr](/content/q821308m37850502/xxlarge945.gif) 1, with approximation order O(h
+ +1/2
) for 0![le](/content/q821308m37850502/xxlarge8804.gif) ![agr](/content/q821308m37850502/xxlarge945.gif) 1/2 andO(h
+1
|ln h| 1/2, for 1/2 #x2264;![agr](/content/q821308m37850502/xxlarge945.gif) 1.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 8–16, 1988. |
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Keywords: | |
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