Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)
From MaRDI portal
Publication:1157107
DOI10.1007/BF01932842zbMath0469.65048OpenAlexW2020345874MaRDI QIDQ1157107
Publication date: 1981
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf01932842
Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)
Related Items
Stability of Runge-Kutta-Nyström methods ⋮ A new finite difference method with optimal phase and stability properties for problems in chemistry ⋮ Efficient FinDiff algorithm with optimal phase properties for problems in quantum chemistry ⋮ New FD methods with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮ A new method with vanished phase-lag and its derivatives of the highest order for problems in quantum chemistry ⋮ A new FinDiff numerical scheme with phase-lag and its derivatives equal to zero for periodic initial value problems ⋮ New FD scheme with vanished phase-lag and its derivatives up to order six for problems in chemistry ⋮ A new algorithm with eliminated phase-lag and its derivatives up to order five for problems in quantum chemistry ⋮ An explicit Numerov-type method for second-order differential equations with oscillating solutions ⋮ A multistep method with optimal phase and stability properties for problems in quantum chemistry ⋮ A multistep conditionally P-stable method with phase properties of high order for problems in quantum chemistry ⋮ Trigonometrically-fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics ⋮ Nyström methods and singular second-order differential equations ⋮ A phase-fitting and first derivative phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮ A phase-fitting, first and second derivatives phase-fitting singularly P-stable economical two-step method for problems in chemistry ⋮ A phase-fitting, first, second and third derivatives phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮ A phase fitted FiniteDiffr process for DiffrntEqutns in chemistry ⋮ A complete in phase FiniteDiffrnc algorithm for DiffrntEqutins in chemistry ⋮ Full in phase finite difference algorithm for differential equations in quantum chemistry ⋮ Solution of quantum chemical problems using an extremely successful and reasonably cost two-step, fourteenth-order phase-fitting approach ⋮ Solution of quantum chemical problems by a very effective and relatively inexpensive two-step, fourteenth-order, phase-fitting procedure ⋮ Families of fifth order Nyström methods for y=f(x,y) and intervals of periodicity ⋮ Phase-fitting, singularly P-stable, cost-effective two-step approach to solving problems in quantum chemistry with vanishing phase-lag derivatives up to order 6 ⋮ A New Optimality Property of Strang’s Splitting ⋮ Two-step extended RKN methods for oscillatory systems ⋮ Two-step, fourteenth-order, phase-fitting procedure with high efficiency and minimal cost for chemical problems ⋮ Highly efficient, singularly P-stable, and low-cost phase-fitting two-step method of 14th order for problems in chemistry ⋮ An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues ⋮ Phase fitted algorithm for problems in quantum chemistry ⋮ A finite difference method with zero phase-lag and its derivatives for quantum chemistry problems ⋮ Complete in phase method for problems in chemistry ⋮ A finite difference method with phase-lag and its derivatives equal to zero for problems in chemistry ⋮ Solution to quantum chemistry problems using a phase-fitting, singularly P-stable, cost-effective two-step approach with disappearing phase-lag derivatives up to order 5 ⋮ The application of explicit Nyström methods to singular second order differential equations ⋮ Explicit Numerov type methods with reduced number of stages. ⋮ EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs ⋮ Two-step method with vanished phase-lag and its derivatives for problems in quantum chemistry: an economical case ⋮ An economical two-step method with optimal phase and stability properties for problems in chemistry ⋮ On the linear stability of splitting methods ⋮ Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation ⋮ Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\) ⋮ A trigonometrically fitted explicit Numerov-type method for second-order initial value problems with oscillating solutions ⋮ Order reduction and how to avoid it when explicit Runge-Kutta-Nyström methods are used to solve linear partial differential equations ⋮ An accomplished phase FD process for DEs in chemistry ⋮ A comparison of symplectic and Hamilton's principle algorithms for autonomous and non-autonomous systems of ordinary differential equations ⋮ A new economical method with eliminated phase-lag and its derivative for problems in chemistry ⋮ A new method with improved phase-lag and stability properties for problems in quantum chemistry - an economical case ⋮ An economical two-step method with improved phase and stability properties for problems in chemistry ⋮ A new improved economical finite difference method for problems in quantum chemistry ⋮ An integrated in phase FD procedure for DiffEqns in chemical problems ⋮ A phase fitted FinDiff process for DifEquns in quantum chemistry ⋮ A complete in phase FinitDiff procedure for DiffEquns in chemistry ⋮ Accuracy and linear stability of RKN methods for solving second-order stiff problems ⋮ NUMEROV-TYPE METHODS FOR OSCILLATORY LINEAR INITIAL VALUE PROBLEMS ⋮ A PHASE-FITTED AND AMPLIFICATION-FITTED EXPLICIT TWO-STEP HYBRID METHOD FOR SECOND-ORDER PERIODIC INITIAL VALUE PROBLEMS ⋮ A phase-fitting singularly P-stable economical two-step method for problems in quantum chemistry ⋮ A singularly P-stable two-step method with improved characteristics for problems in chemistry ⋮ Phase fitted method for quantum chemistry problems ⋮ A phase-fitting singularly P-stable cost-effective two-step method for solving chemistry problems ⋮ High-order zero-dissipative Runge-Kutta-Nyström methods ⋮ A perfect in phase FD algorithm for problems in quantum chemistry ⋮ Embedded implicit Runge–Kutta Nyström method for solving second-order differential equations ⋮ A class of explicit two-step hybrid methods for second-order IVPs ⋮ A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems ⋮ Absolute stability of explicit Runge-Kutta-Nyström methods for \(y=f(x,y,y')\) ⋮ Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström- Runge-Kutta-Methoden (Nonlinear stability and phase analysis for adaptive Nyström-Runge-Kutta methods) ⋮ A new class of explicit two-step fourth order methods for \(y=f(t,y)\) with extended intervals of periodicity ⋮ A two-step method singularly P-Stable with improved properties for problems in quantum chemistry ⋮ A two-step singularly P-Stable method with high phase and large stability properties for problems in chemistry
Cites Work
- Méthodes de Nystrom pour l'équation différentielle y=f(x,y)
- Unconditionally stable methods for second order differential equations
- Stabilization of Cowell's method
- Stabilized Runge–Kutta Methods for Second Order Differential Equations without First Derivatives
- Modified Nyström Methods for Semi-discrete Hyperbolic Differential Equations
- Symmetric Multistip Methods for Periodic Initial Value Problems
- [https://portal.mardi4nfdi.de/wiki/Publication:4168001 Complete Characterization of Multistep Methods with an Interval of Periodicity for Solving y � � = f(x,y)]
- Zur Stabilität des Nyströmschen Verfahrens I
This page was built for publication: Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)