Abstract
Using the rational splitting of a cosine operator-function, the fourth order accuracy decomposition scheme is constructed for hyperbolic equation when the principal operator is self-adjoint positively defined and is represented as a sum of two summands. Stability of the constructed scheme is shown and the error of an approximate solution is estimated.
Abstract
In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation
𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢)
with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered.
Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.
The Existence of a Global Attractor for one Fourth Order Hyperbolic Equation with Memory Operator