Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems

DOI10.1007/s11075-020-00976-9zbMath1465.65059OpenAlexW3044392373MaRDI QIDQ2028021

Ch. Tsitouras, Theodore E. Simos

Publication date: 31 May 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-020-00976-9

zbMATH Keywords

initial value problemRunge-Kutta methodsorder conditionsdifferential evolutionlinear inhomogeneous problem

Mathematics Subject Classification ID

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

Related Items (3)

A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation ⋮ Runge–Kutta pairs of orders 8(7) with extended stability regions for addressing linear inhomogeneous systems ⋮ Runge-Kutta-Nyström methods of eighth order for addressing linear inhomogeneous problems

Uses Software

• Matlab
• EXPODE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A family of embedded Runge-Kutta formulae
• A P-stable singly diagonally implicit Runge-Kutta-Nyström method
• Runge-Kutta pairs for periodic initial value problems
• Differential evolution -- a simple and efficient heuristic for global optimization over continuous spaces
• Trigonometric-fitted explicit Numerov-type method with vanishing phase-lag and its first and second derivatives
• Runge-Kutta methods for linear ordinary differential equations
• Global error estimation with Runge-Kutta triples
• High algebraic, high phase-lag order embedded Numerov-type methods for oscillatory problems
• Explicit two-step methods for second-order linear IVPs
• A tenth-order symplectic Runge-Kutta-Nyström method
• Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\)
• Explicit Runge-Kutta methods for starting integration of Lane-Emden problem
• Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits
• Evolutionary derivation of sixth-order P-stable SDIRKN methods for the solution of PDEs with the method of lines
• Symbolic derivation of Runge-Kutta order conditions
• Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
• Displacement and frequency analyses of vibratory systems
• Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs
• Some Practical Runge-Kutta Formulas
• The efficient solution of linear constant-coefficient systems of differential equations
• Fitted modifications of Runge‐Kutta pairs of orders 6(5)
• Trigonometric–fitted hybrid four–step methods of sixth order for solving
• Cheap Error Estimation for Runge--Kutta Methods
• A General Family of Explicit Runge–Kutta Pairs of Orders $6(5)$
• Ninth‐order, explicit, two‐step methods for second‐order inhomogeneous linear IVPs
• Error estimates for Runge-Kutta type solutions to systems of ordinary differential equations
• On Runge-Kutta processes of high order
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems
• Implicit Runge-Kutta Processes

This page was built for publication: Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems