Explicit Numerov type methods with reduced number of stages.

DOI10.1016/S0898-1221(03)80005-6zbMath1035.65078MaRDI QIDQ1416371

Ch. Tsitouras

Publication date: 14 December 2003

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

zbMATH Keywords

Initial value problemNumerical resultsHybrid methodshybrid explicit Numerov type methodsTwo step methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (27)

Explicit two-step methods for second-order linear IVPs ⋮ An explicit Numerov-type method for second-order differential equations with oscillating solutions ⋮ On ninth order, explicit Numerov-type methods with constant coefficients ⋮ A new eighth order exponentially fitted explicit Numerov-type method for solving oscillatory problems ⋮ Multi-step hybrid methods for special second-order differential equations \(y^{\prime \prime}(t)=f(t,y(t))\) ⋮ Phase-fitted Numerov type methods ⋮ Extended RKN-type methods with minimal dispersion error for perturbed oscillators ⋮ Two-step extended RKN methods for oscillatory systems ⋮ Quadratic Störmer-type methods for the solution of the Boussinesq equation by the method of lines ⋮ EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs ⋮ Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\) ⋮ Explicit exponentially fitted two-step hybrid methods of high order for second-order oscillatory IVPs ⋮ Piecewise-linearized methods for initial-value problems with oscillating solutions ⋮ Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\) ⋮ Phase-fitted and amplification-fitted two-step hybrid methods for \(y^{\prime\prime }=f(x,y)\) ⋮ Optimization of explicit two-step hybrid methods for solving orbital and oscillatory problems ⋮ Stage reduction on P-stable Numerov type methods of eighth order ⋮ Trigonometrically fitted explicit Numerov-type method for periodic IVPs with two frequencies ⋮ Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits ⋮ Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives ⋮ Multi-step Runge-Kutta-Nyström methods for special second-order initial value problems ⋮ Scheifele two-step methods for perturbed oscillators ⋮ 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 ⋮ EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS ⋮ A class of explicit two-step hybrid methods for second-order IVPs ⋮ Families of explicit two-step methods for integration of problems with oscillating solutions

Uses Software

• Mathematica
• SLCPM12

Cites Work

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• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
• A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
• Intervals of periodicity and absolute stability of explicit Nyström methods for y=f(x,y)
• Explicit two-step methods with minimal phase-lag for the numerical integration of special second-order initial-value problems and their application to the one-dimensional Schrödinger equation
• Stabilization of Cowell's classical finite difference method for numerical integration
• Explicit high order methods for the numerical integration of periodic initial-value problems
• A conditionally \(P\)-stable fourth-order exponential-fitting method for \(y=f(x,y)\)
• CP methods for the Schrödinger equation revisited
• A \(P\)-stable exponentially fitted method for the numerical integration of the Schrödinger equation
• An exponentially fitted eighth-order method for the numerical solution of the Schrödinger equation
• SLCPM12 -- a program for solving regular Sturm-Liouville problems
• An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
• A tenth-order symplectic Runge-Kutta-Nyström method
• A family of \(P\)-stable exponentially-fitted methods for the numerical solution of the Schrödinger equation
• Families of Runge-Kutta-Nystrom Formulae
• A General Procedure For the Adaptation of Multistep Algorithms to the Integration of Oscillatory Problems
• Zur numerischen Integration von Differentialgleichungen durch Potenzreihen‐Ansätze, dargestellt an Hand physikalischer Beispiele

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