A variable step-size exponentially fitted explicit hybrid method for solving oscillatory problems

DOI10.1155/2011/328197zbMath1236.65082DBLPjournals/ijmmsc/SamatIS11OpenAlexW2143679441WikidataQ58687751 ScholiaQ58687751MaRDI QIDQ763017

F. Samat, Mohamed Bin Suleiman, Fudziah Bt. Ismail

Publication date: 8 March 2012

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2011/328197

zbMATH Keywords

stabilitynumerical experimentsexponential fittingvariable step-sizedifferential systemoscillatory problem

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

Cites Work

• Exponentially fitted two-step hybrid methods for \(y^{\prime\prime} = f(x,y)\)
• A dissipative exponentially-fitted method for the numerical solution of the Schrödinger equation and related problems
• A Runge-Kutta-Nyström pair for the numerical integration of perturbed oscillators
• Trigonometric polynomial or exponential fitting approach?
• New Runge-Kutta-Nyström formula-pairs of order 8(7), 9(8), 10(9) and 11(10) for differential equations of the form \(y=f(x,y)\)
• A P-stable hybrid exponentially-fitted method for the numerical integration of the Schrödinger equation
• Exponentially fitted explicit Runge-Kutta-Nyström methods
• A class of explicit two-step hybrid methods for second-order IVPs
• Families of Runge-Kutta-Nystrom Formulae
• Order conditions for a class of two-step methods for y = f (x, y)
• P-stability and exponential-fitting methods for y = f(x,y)

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