An error analysis of the modified scaling and squaring method

DOI10.1016/j.camwa.2006.04.032zbMath1134.65053OpenAlexW2075057073MaRDI QIDQ2468911

S. Koikari

Publication date: 30 January 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.04.032

zbMATH Keywords

algorithmnumerical examplesrational approximationmatrix exponentialexponential integrators\(\varphi\)-functiontruncation error analysisrounding error analysis

Mathematics Subject Classification ID

Roundoff error (65G50) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

The complex step approximation to the Fréchet derivative of a matrix function ⋮ Exponential time differencing for the tracer equations appearing in primitive equation ocean models ⋮ Exponential Runge-Kutta parareal for non-diffusive equations ⋮ Unnamed Item ⋮ Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation ⋮ A Class of Exponential Integrators Based on Spectral Deferred Correction ⋮ Comparison of methods for evaluating functions of a matrix exponential ⋮ The scaling and modified squaring method for matrix functions related to the exponential

Uses Software

• mctoolbox
• Expint
• testmatrix
• MATLAB expm
• apfloat

Cites Work

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• On Logarithmic Norms
• Numerical Computation of the Matrix Exponential with Accuracy Estimate
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Exponential Integrators for Large Systems of Differential Equations
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Fourth-Order Time-Stepping for Stiff PDEs