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   Articles with "two derivative" as a keyword



Modified two-derivative Runge–Kutta methods for the Schrödinger equation

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recommendations! Published in 2017 at "Journal of Mathematical Chemistry"

DOI: 10.1007/s10910-017-0830-0

Abstract: A family of modified two-derivative Runge–Kutta (MTDRK) methods for the integration of the Schrödinger equation are obtained. Two new three-stage and fifth order TDRK methods are derived. The numerical results in the integration of the… read more here.

Keywords: dinger equation; derivative runge; modified two; two derivative ... See more keywords

Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations

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recommendations! Published in 2019 at "Applied Numerical Mathematics"

DOI: 10.1016/j.apnum.2019.03.006

Abstract: Abstract A new family of modified two-derivative Runge-Kutta-Nystrom (TDRKN) methods are proposed for solving initial value problems of second-order oscillatory ordinary differential equations. Order conditions are obtained via the Nystrom tree theory and the B-series… read more here.

Keywords: runge kutta; derivative runge; order oscillatory; order ... See more keywords

Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nyström Methods for Solving

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recommendations! Published in 2018 at "Mathematical Problems in Engineering"

DOI: 10.1155/2018/7689854

Abstract: Two exponentially fitted and trigonometrically fitted explicit two-derivative Runge-Kutta-Nystrom (TDRKN) methods are being constructed. Exponentially fitted and trigonometrically fitted TDRKN methods have the favorable feature that they integrate exactly second-order systems whose solutions are linear… read more here.

Keywords: exponentially fitted; fitted trigonometrically; trigonometrically fitted; derivative runge ... See more keywords

Two-Derivative Runge-Kutta Methods with Frequency Dependent Coefficients for Solving Orbital or Oscillatory Problems

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recommendations! Published in 2025 at "Algorithms"

DOI: 10.3390/a18100603

Abstract: In this work, explicit Two-Derivative Runge–Kutta methods of the general case (that use several evaluations of the right-hand side function and its derivative per step) are considered. In order to address problems of orbital or… read more here.

Keywords: runge kutta; two derivative; orbital oscillatory; kutta methods ... See more keywords

High-Order Special Two-Derivative Runge–Kutta Pairs

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recommendations! Published in 2025 at "Mathematics"

DOI: 10.3390/math13223676

Abstract: This paper presents the development and analysis of novel explicit special two-derivative Runge–Kutta (STDRK) pairs for the numerical integration of ordinary differential equations (ODEs), with a focus on achieving seventh-order accuracy and embedded fifth-order error… read more here.

Keywords: two derivative; special two; order; runge kutta ... See more keywords

High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error

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recommendations! Published in 2021 at "Mathematics"

DOI: 10.3390/math9030232

Abstract: In this work we consider explicit Two-derivative Runge-Kutta methods of a specific type where the function f is evaluated only once at each step. New 7th order methods are presented with minimized dispersion and dissipation… read more here.

Keywords: runge kutta; derivative runge; kutta methods; order ... See more keywords