On ninth order, explicit Numerov-type methods with constant coefficients
From MaRDI portal
Publication:1635740
DOI10.1007/s00009-018-1089-9zbMath1446.65046OpenAlexW2793224691MaRDI QIDQ1635740
Ch. Tsitouras, Theodore E. Simos
Publication date: 1 June 2018
Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00009-018-1089-9
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)
New three-stages symmetric six-step finite difference method with vanished phase-lag and its derivatives up to sixth derivative for second order initial and/or boundary value problems with periodical and/or oscillating solutions ⋮ New Runge-Kutta type symmetric two-step method with optimized characteristics ⋮ A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation ⋮ New multiple stages multistep method with best possible phase properties for second order initial/boundary value problems ⋮ New four stages multistep in phase algorithm with best possible properties for second order problems ⋮ New multistage two-step complete in phase scheme with improved properties for quantum chemistry problems ⋮ A new multistage multistep full in phase algorithm with optimized characteristics for problems in chemistry ⋮ An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems ⋮ Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines ⋮ The new class of multistep multiderivative hybrid methods for the numerical solution of chemical stiff systems of first order IVPs ⋮ New four-stages symmetric six-step method with improved phase properties for second order problems with periodical and/or oscillating solutions ⋮ A new multistep method with optimized characteristics for initial and/or boundary value problems ⋮ New three-stages symmetric two step method with improved properties for second order initial/boundary value problems ⋮ New hybrid symmetric two step scheme with optimized characteristics for second order problems ⋮ Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\) ⋮ A four-stages multistep fraught in phase method for quantum chemistry problems ⋮ Explicit, eighth-order, four-step methods for solving \(y^{\prime\prime}=f(x, y)\) ⋮ Explicit Runge-Kutta methods for starting integration of Lane-Emden problem ⋮ 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 ⋮ Neural network solution of single-delay differential equations ⋮ Eighth order, phase-fitted, six-step methods for solving \(y^{\prime \prime}=f(x,y)\) ⋮ Algorithm for the development of families of numerical methods based on phase-lag Taylor series ⋮ A Runge-Kutta type crowded in phase algorithm for quantum chemistry problems ⋮ A perfect in phase FD algorithm for problems in quantum chemistry ⋮ A multiple stage absolute in phase scheme for chemistry problems ⋮ Bounds for variable degree rational \(L_\infty\) approximations to the matrix exponential
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A new approach on the construction of trigonometrically fitted two step hybrid methods
- Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods
- An optimized two-step hybrid block method for solving general second order initial-value problems
- A new phase-fitted eight-step symmetric embedded predictor-corrector method (EPCM) for orbital problems and related IVPs with oscillating solutions
- A high-order two-step phase-fitted method for the numerical solution of the Schrödinger equation
- A new optimized symmetric 8-step semi-embedded predictor-corrector method for the numerical solution of the radial Schrödinger equation and related orbital problems
- The use of phase lag and amplification error derivatives for the construction of a modified Runge-Kutta-Nyström method
- A new family of symmetric linear four-step methods for the efficient integration of the Schrödinger equation and related oscillatory problems
- A parametric symmetric linear four-step method for the efficient integration of the Schrödinger equation and related oscillatory problems
- New stable closed Newton-Cotes trigonometrically fitted formulae for long-time integration
- Optimizing a hybrid two-step method for the numerical solution of the Schrödinger equation and related problems with respect to phase-lag
- An eight-step semi-embedded predictor-corrector method for orbital problems and related IVPs with oscillatory solutions for which the frequency is unknown
- New modified Runge-Kutta-Nyström methods for the numerical integration of the Schrödinger equation
- Construction of an optimized explicit Runge-Kutta-Nyström method for the numerical solution of oscillatory initial value problems
- On modified Runge-Kutta trees and methods
- A \(P\)-stable eighth-order method for the numerical integration of periodic initial-value problems
- Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
- Runge-Kutta interpolants based on values from two successive integration steps
- Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\)
- Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation
- A family of trigonometrically fitted partitioned Runge-Kutta symplectic methods
- High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation
- Symbolic derivation of Runge-Kutta-Nyström order conditions
- Numerov made explicit has better stability
- A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
- High order P-stable formulae for the numerical integration of periodic initial value problems
- Unconditionally stable methods for second order differential equations
- Explicit high order methods for the numerical integration of periodic initial-value problems
- Runge-Kutta pairs for periodic initial value problems
- Eighth-order methods for elastic scattering phase shifts
- Zero dissipative, explicit Numerov-type methods for second order IVPs with oscillating solutions
- Explicit Numerov type methods with reduced number of stages.
- Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions
- Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs
- An explicit sixth-order method with phase-lag of order eight for \(y=f(t,y)\)
- Explicit two-step methods for second-order linear IVPs
- Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs
- Phase-fitted Runge-Kutta pairs of orders 8(7)
- A family of high-order multistep methods with vanished phase-lag and its derivatives for the numerical solution of the Schrödinger equation
- A parameter study of explicit Runge-Kutta pairs of orders 6(5)
- Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs
- A new family of 7 stages, eighth-order explicit Numerov-type methods
- EXPLICIT EIGHTH ORDER NUMEROV-TYPE METHODS WITH REDUCED NUMBER OF STAGES FOR OSCILLATORY IVPs
- NUMEROV-TYPE METHODS FOR OSCILLATORY LINEAR INITIAL VALUE PROBLEMS
- A one-step method for direct integration of structural dynamic equations
- Symmetric Multistip Methods for Periodic Initial Value Problems
- High-Order Symplectic Runge–Kutta–Nyström Methods
- Modified two‐step hybrid methods for the numerical integration of oscillatory problems
- Order conditions and symmetry for two-step hybrid methods
- High Phase-Lag-Order Runge--Kutta and Nyström Pairs
- Order conditions for a class of two-step methods for y = f (x, y)
- A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation
- EXPLICIT EIGHTH ORDER TWO-STEP METHODS WITH NINE STAGES FOR INTEGRATING OSCILLATORY PROBLEMS
- On Runge-Kutta processes of high order
- Implicit Runge-Kutta Processes
- Conditions for Trigonometrically Fitted Runge-Kutta Methods
- Two-step fourth order P-stable methods for second order differential equations
- Dissipative high phase-lag order methods
This page was built for publication: On ninth order, explicit Numerov-type methods with constant coefficients