Numerical Integrators for Stiff and Highly Oscillatory Differential Equations
نویسندگان
چکیده
منابع مشابه
Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review
Numerical methods for oscillatory, multi-scale Hamiltonian systems are reviewed. The construction principles are described, and the algorithmic and analytical distinction between problems with nearly constant high frequencies and with timeor state-dependent frequencies is emphasized. Trigonometric integrators for the first case and adiabatic integrators for the second case are discussed in more...
متن کاملThe Accurate Numerical Solution of Highly Oscillatory Ordinary Differential Equations*
An asymptotic theory for weakly nonlinear, highly oscillatory systems of ordinary differential equations leads to methods which are suitable for accurate computation with large time steps. The theory is developed for systems of the form Z = (A(t)/e)Z + H(Z,t). Z(0, f) = Z„, 0</< 7\0<e« 1, where the diagonal matrix A(t) has smooth, purely imaginary eigenvalues and the components of H(Z, i) are p...
متن کاملAdiabatic Integrators for Highly Oscillatory Second-order Linear Differential Equations with Time-varying Eigendecomposition
Numerical integrators for second-order differential equations with time-dependent high frequencies are proposed and analysed. We derive two such methods, called the adiabatic midpoint rule and the adiabatic Magnus method. The integrators are based on a transformation of the problem to adiabatic variables and an expansion technique for the oscillatory integrals. They can be used with far larger ...
متن کاملUniformly Accurate Multiscale Time Integrators for Highly Oscillatory Second Order Differential Equations
In this paper, two multiscale time integrators (MTIs), motivated from two types of multiscale decomposition by either frequency or frequency and amplitude, are proposed and analyzed for solving highly oscillatory second order differential equations with a dimensionless parameter 0< ε≤ 1. In fact, the solution to this equation propagates waves with wavelength atO(ε2)when 0<ε≪1, which brings sign...
متن کاملNumerical integrators based on modified differential equations
Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formula...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1980
ISSN: 0025-5718
DOI: 10.2307/2006091