Modified two-derivative Runge–Kutta methods for the Schrödinger equation
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
Sign Up to like & getrecommendations! 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
High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error
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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