The Bitsadze‐Samarskii type nonlocal boundary value problem
{−d2u(t)dt2+Au(t) = f(t), 0<t<1,u(0) = φ, u(1) =  ∑ j = 1Jαju(λj)+ψ, ∑ j = 1J|αj|≤1, 0<λ1<λ2<⋯<λJ<1
for the differential equation in a Hilbert space H with the self‐adjoint positive definite operator A is considered. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well posedness of this difference scheme in difference analogue of Hölder spaces is established.
Topics
Hilbert space
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© 2011 American Institute of Physics.
2011
American Institute of Physics
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