As it is known the equation Aϕ = f with injective compact operator has a unique solution for all f in the range R(A).Unfortunately, the righthand side f is never known exactly, so we can take an approximate data fδ and used the perturbed problem αϕ + Aϕ = fδ where the solution ϕαδ depends continuously on the data fδ, and the bounded inverse operator (αI + A)−1 approximates the unbounded operator A−1 but not stable. In this work we obtain the convergence of the approximate solution of ϕαδ of the perturbed equation to the exact solution ϕ of initial equation provided α tends to zero with δ/√α.
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Citation
Noui DJAIDJA ,
Mostefa NADIR ,
, (2021), Comparison between Taylor and perturbed method for Volterra integral equation of the first kind, Numerical Algebra, Control and Optimization,
Vol:11, Issue:4, pages:487-493, American Institute of Mathematical Sciences
