Explicit, ninth order, two step methods for solving inhomogeneous linear problems \(x(t)= \Lambda x(t)+f(t)\)

DOI10.1016/j.apnum.2020.03.003zbMath1436.65085OpenAlexW3010093941MaRDI QIDQ1986165

Ch. Tsitouras, Theodore E. Simos

Publication date: 7 April 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.03.003

zbMATH Keywords

initial value problemnumerical solutionhybrid methods

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (4)

A new implicit high-order six-step singularly P-stable method for the numerical solution of Schrödinger equation ⋮ New family for Runge‐Kutta‐Nyström pairs of orders 6(4) with coefficients trained to address oscillatory problems ⋮ Runge–Kutta pairs of orders 8(7) with extended stability regions for addressing linear inhomogeneous systems ⋮ Evolutionary derivation of Runge-Kutta pairs for addressing inhomogeneous linear problems

Uses Software

• Mathematica
• numerov
• NEW9p

Cites Work

• Symbolic derivation of order conditions for hybrid Numerov-type methods solving \(y^{\prime\prime} =f(x,y)\)
• Symbolic derivation of Runge-Kutta-Nyström order conditions
• Explicit Numerov type methods with reduced number of stages.
• 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
• Runge-Kutta methods for linear ordinary differential equations
• Explicit two-step methods for second-order linear IVPs
• Hybrid Numerov-type methods with coefficients trained to perform better on classical orbits
• Evolutionary generation of high-order, explicit, two-step methods for second-order linear IVPs
• The efficient solution of linear constant-coefficient systems of differential equations
• High Phase-Lag-Order Runge--Kutta and Nyström Pairs
• Ninth‐order, explicit, two‐step methods for second‐order inhomogeneous linear IVPs
• On Runge-Kutta processes of high order
• Implicit Runge-Kutta Processes

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