Convergence Analysis of an Extended Krylov Subspace Method for the Approximation of Operator Functions in Exponential Integrators

DOI10.1137/12089226XzbMath1278.65076MaRDI QIDQ2855104

Publication date: 24 October 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

convergence evolution equation semigroup rational approximation operator functions matrix function $\varphi$-functions extended Krylov subspace method exponential integrator rational Krylov subspace method

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical solutions to abstract evolution equations (65J08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (14)

A study of defect-based error estimates for the Krylov approximation of $\varphi$-functions ⋮ A framework of the harmonic Arnoldi method for evaluating $\varphi$-functions with applications to exponential integrators ⋮ Efficient time integration for discontinuous Galerkin approximations of linear wave equations ⋮ An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains ⋮ Acceleration of contour integration techniques by rational Krylov subspace methods ⋮ Avoiding order reduction when integrating reaction-diffusion boundary value problems with exponential splitting methods ⋮ Adaptive Rational Krylov Methods for Exponential Runge–Kutta Integrators ⋮ Computing Semigroups with Error Control ⋮ APPROXIMATION OF THE LINEAR COMBINATION OF <i>φ</i>-FUNCTIONS USING THE BLOCK SHIFT-AND-INVERT KRYLOV SUBSPACE METHOD ⋮ Exponential Quadrature Rules Without Order Reduction for Integrating Linear Initial Boundary Value Problems ⋮ Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces ⋮ A conjugate-gradient-type rational Krylov subspace method for ill-posed problems ⋮ Higher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part I: Stability ⋮ Automatic Smoothness Detection of the Resolvent Krylov Subspace Method for the Approximation of $C_0$-Semigroups

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