Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces

DOI10.1090/S0025-5718-04-01720-XzbMath1066.65061OpenAlexW2090581346MaRDI QIDQ4654011

Volodymyr L. Makarov, Ivan P. Gavrilyuk

Publication date: 1 March 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01720-x

zbMATH Keywords

convergenceBanach spaceserror estimationparallel computationHilbert spacesoperator cosine functionabstract parabolic evolution equationoperator exponentialabsolutely convergent algorithmsparameter depended operatorSinc-methodsSinc-quadrature

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Parallel numerical computation (65Y05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Numerical solutions to equations with linear operators (65J10) Linear differential equations in abstract spaces (34G10) Abstract hyperbolic equations (35L90)

Related Items (4)

The Cayley Transform as a Time Discretization Scheme ⋮ On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems ⋮ Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions ⋮ An exponentially convergent algorithm for nonlinear differential equations in Banach spaces

Cites Work

• Semigroups of linear operators and applications to partial differential equations
• Finite difference methods (Part 1). Solution of equations in \(R^ n\) (Part 1)
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Strongly \(P\)-positive operators and explicit representations of the solutions of initial value problems for second-order differential equations in Banach space
• \(\mathcal H\)-matrix approximation for the operator exponential with applications
• Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach spaces
• A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
• Stability and Regularization of Three-Level Difference Schemes with Unbounded Operator Coefficients in Banach Spaces
• Exponentially Convergent Parallel Discretization Methods for the First Order Evolution Equations
• Data-sparse approximation to the operator-valued functions of elliptic operator
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