Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines
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Publication:2424111
DOI10.1007/s00009-019-1336-8zbMath1415.65150OpenAlexW2935826836WikidataQ114232316 ScholiaQ114232316MaRDI QIDQ2424111
Ch. Tsitouras, Jwu Jenq Chen, Chia-Liang Lin, Theodore E. Simos
Publication date: 24 June 2019
Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00009-019-1336-8
Approximation methods and heuristics in mathematical programming (90C59) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for stiff equations (65L04)
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- 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 high-order two-step phase-fitted method for the numerical solution of the Schrödinger equation
- 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
- Closed Newton-Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
- Stability of collocation-based Runge-Kutta-Nyström methods
- Stability of Runge-Kutta-Nyström methods
- 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
- High order closed Newton-Cotes trigonometrically-fitted formulae for the numerical solution of the Schrödinger equation
- Symbolic derivation of Runge-Kutta-Nyström order conditions
- A P-stable singly diagonally implicit Runge-Kutta-Nyström method
- Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
- On ninth order, explicit Numerov-type methods with constant coefficients
- Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives
- 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
- Stage reduction on P-stable Numerov type methods of eighth order
- Symbolic derivation of Runge-Kutta order conditions
- 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
- Two-stage and Three-stage Diagonally Implicit Runge-Kutta Nyström Methods of Orders Three and Four
- Quadratic Störmer-type methods for the solution of the Boussinesq equation by the method of lines
- A Compendium of Partial Differential Equation Models
- Diagonally Implicit Runge–Kutta–Nyström Methods for Oscillatory Problems
- Fitted modifications of Runge‐Kutta pairs of orders 6(5)
- Fitted modifications of classical Runge‐Kutta pairs of orders 5(4)
- Trigonometric–fitted hybrid four–step methods of sixth order for solving
- Trigonometric fitted, eighth‐order explicit Numerov‐type methods
- Linearized numerical schemes for the Boussinesq equation
- High Phase-Lag-Order Runge--Kutta and Nyström Pairs
- A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation
- Hybrid, phase–fitted, four–step methods of seventh order for solving x″(t) = f(t,x)
- On Runge-Kutta processes of high order
- Implicit Runge-Kutta Processes
- Four-stage symplectic and P-stable SDIRKN methods with dispersion of high order
- Optimized explicit Runge-Kutta pair of orders \(9(8)\)