Allaberen Ashyralyev

Learn More
The stable difference scheme for the approximate solution of the initial value problem () () () () 1 2 , t du t D u t Au t f t dt + + = () 0 1, 0 0 t u < < = for the differential equation in a Banach space E with the strongly positive operator A and fractional operator 1 2 t D is presented. The well-posedness of the difference scheme in difference analogues(More)
The abstract nonlocal boundary value problem      − d 2 u(t) dt 2 + sign(t)Au(t) = g(t), (0 ≤ t ≤ 1), du(t) dt + sign(t)Au(t) = f (t), (−1 ≤ t ≤ 0), u(1) = u(−1) + µ for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in Hölder spaces without a weight is(More)
The initial-value problem for hyperbolic equation d2u(t)/dt2 +A(t)u(t) = f (t) (0 ≤ t ≤ T), u(0) = φ,u(0) = ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution(More)
We consider the abstract Cauchy problem for differential equation of the hyperbolic type v′′(t) + Av(t) = f (t) (0 ≤ t ≤ T), v(0) = v0, v′(0) = v′ 0 in an arbitrary Hilbert space H with the selfadjoint positive definite operator A. The high order of accuracy two-step difference schemes generated by an exact difference scheme or by the Taylor decomposition(More)
It is well known the differential equation −u (t) + Au(t) = f (t) (−∞ < t < ∞) in a general Banach space E with the positive operator A is ill-posed in the Banach space C(E) = C((−∞,∞),E) of the bounded continuous functions ϕ(t) defined on the whole real line with norm ϕ C(E) = sup −∞<t<∞ ϕ(t) E. In the present paper we consider the high order of accuracy(More)
The abstract nonlocal boundary value problem −d 2 ut/dt 2 Aut gt, 0 < t < 1, dut/dt − Aut ft, 1 < t < 0, u1 u−1 μ for differential equations in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well-posedness of this problem in H ¨ older spaces with a weight is established. The coercivity inequalities for the solution(More)
and Applied Analysis 3 2. Difference Schemes: Well-Posedness The discretization of problem 1.2 is carried out in two steps. In the first step let us define the grid sets as follows: Ω̃h {x : x xm h1m1, . . . , hnmn , m m1, . . . , mn , 0 ≤ mr ≤ Nr, hrNr L, r 1, . . . , n} Ωh Ω̃h ∩Ω, Sh Ω̃h ∩ S. 2.1 We introduce the Hilbert space L2h L2 Ω̃h of the grid(More)