Dynamical systems method for solving operator equations
نویسندگان
چکیده
منابع مشابه
Dynamical Systems Method for Solving Operator Equations
Consider an operator equation F(u)=0 in a Hilbert space H and assume that this equation is solvable. Let us call the problem of solving this equation ill-posed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. A general method, Dynamical Systems Method (DSM), for solving linear and nonlinear illposed problems in H is presented. This method consists of the constructio...
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Consider an operator equation (*) B(u) + u = 0 in a real Hilbert space, where > 0 is a small constant. The DSM (Dynamical Systems Method) for solving equation (*) consists of finding and solving a Cauchy problem: u̇ = Φ(t, u), u(0) = u0, t ≥ 0, which has the following properties: 1) it has a global solution u(t), 2) this solution tends to a limit as time tends to infinity, i.e., u(∞) exists, 3) ...
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The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical mod...
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Let F (u) = h be an operator equation in a Banach space X with Gateaux differentiable norm, ‖F ′(u) − F ′(v)‖ ≤ ω(‖u − v‖), where ω ∈ C([0,∞)), ω(0) = 0, ω(r) is strictly growing on [0,∞). Denote A(u) := F ′(u), where F ′(u) is the Fréchet derivative of F , and Aa := A + aI. Assume that (*) ‖A−1 a (u)‖ ≤ c1 |a|b , |a| > 0, b > 0, a ∈ L. Here a may be a complex number, and L is a smooth path on ...
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2004
ISSN: 1007-5704
DOI: 10.1016/s1007-5704(03)00006-6