Asymptotic estimates of a projection-difference method for an operator-differential equation

作者：Vinogradova P V^*; Zarubin A G

来源：Journal of Numerical Mathematics, 2013, 21(3): 181-200.

DOI：10.1515/jnum-2013-0008

• Cauchy problem
• difference scheme
• operator-differential equation
• Petrov-Galerkin method
• Hilbert space
• orthogonal projection
• convergence rate

In the current paper, we study a Petrov-Galerkin method for a Cauchy problem for an operator-differential equation with a leading self-adjoint operator A and a subordinate linear operator K(t) in a Hilbert space. Error estimates for the approximate solutions are obtained. We consider the full equation discretization based on a two-level difference scheme. New asymptotic estimates for the convergence rate of approximate solutions are obtained in uniform topology. The method is applied to the model parabolic problems.

• 出版日期2013-10