A higher order local linearization method for solving ordinary differential equations

DOI10.1016/j.amc.2006.06.096zbMath1115.65080OpenAlexW1995014455MaRDI QIDQ870151

Tohru Ozaki, F. Carbonell, J. C. Jimenez, R. J. Biscay, H. de la Cruz

Publication date: 12 March 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.06.096

zbMATH Keywords

comparison of methodsnumerical experimentsinitial value problemsTaylor expansionexponential methodsvariation of constants formulafirst order differential systemshyperbolic stationary pointslinearization of the local solution

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

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Uses Software

• Expokit
• RODAS
• ATOMFT
• MATLAB expm

Cites Work

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• Exponential time differencing for stiff systems
• Solving linear ordinary differential equations by exponentials of iterated commutators
• On the implementation of the method of Magnus series for linear differential equations
• A matricial exponentially fitted scheme for the numerical solution of stiff initial-value problems
• ATOMFT: Solving ODEs and DAEs using Taylor series
• Piecewise-linearized methods for initial-value problems
• Local linearization method for the numerical solution of stochastic differential equations
• Improved high order integrators based on the Magnus expansion
• A simple algebraic expression to evaluate the local linearization schemes for stochastic differential equations
• Exponential Runge-Kutta methods for parabolic problems.
• Dynamic properties of the local linearization method for initial value problems.
• Padé approximation for the exponential of a block triangular matrix
• Computing multiple integrals involving matrix exponentials
• Rate of convergence of local linearization schemes for initial-value problems
• The local linearization method for numerical integration of random differential equations
• Methods for the approximation of the matrix exponential in a Lie-algebraic setting
• Solving Ordinary Differential Equations I
• Local Linearization-Runge Kutta (LLRK) Methods for Solving Ordinary Differential Equations
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• The method of local linearization in the numerical solution of stiff systems of ordinary differential equations
• Quadrature Methods for Stiff Ordinary Differential Systems
• Comparing numerical methods for stiff systems of O.D.E:s
• Computing integrals involving the matrix exponential
• Expokit
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Exponential Integrators for Large Systems of Differential Equations
• Approximation of continuous time stochastic processes by the local linearization method revisited
• Fourth-Order Time-Stepping for Stiff PDEs
• Local Linearization Method for Numerical Integration of Delay Differential Equations
• Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
• Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
• Some A-Stable Methods for Stiff Ordinary Differential Equations
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems