COMPARISON BETWEEN TAYLOR AND PERTURBED METHOD FOR VOLTERRA INTEGRAL EQUATION OF THE FIRST KIND
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Date
2020
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Publisher
Université de M'sila
Abstract
As it is known the equation A' = f with injective compact oper-
ator has a unique solution for all f in the range R(A):Unfortunately, the right-
hand side f is never known exactly, so we can take an approximate data f and
used the perturbed problem ' + A' = f where the solution ' depends
continuously on the data f ; and the bounded inverse operator ( I + A)1
approximates the unbounded operator A1 but not stable. In this work we
obtain the convergence of the approximate solution of ' of the perturbed
equation to the exact solution ' of initial equation provided tends to zero
with
p
: