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Derivation of three-derivative Runge-Kutta methods
18/18 checkable references clean · checked 2026-08-10
Every reference with a DOI in the deposited reference list resolved to a known work in Crossref or DataCite at the dated check, and none carried a retraction, withdrawal, or removal notice.
7 without a DOI — not checked. A reference deposited without a DOI is never matched by title or guessed at; it stays outside the checked set, and this line discloses that.
The 18 checked references that resolve
resolves10.1007/s00607-005-0151-1
A Simplified Approach to the Order Conditions of Integration Methods
resolves10.1137/0711029
Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
resolves10.1142/S0129183113500733
EXPONENTIALLY FITTED TWO-DERIVATIVE RUNGE–KUTTA METHODS FOR THE SCHRÖDINGER EQUATION
resolves10.1007/s11075-013-9802-z
Trigonometrically fitted two-derivative Runge-Kutta methods for solving oscillatory differential equations
resolves10.1007/BF02252917
Multistep-multistage-multiderivative methods for ordinary differential equations
resolves10.1093/comjnl/5.4.329
Some general implicit processes for the numerical solution of differential equations
The 7 references without a DOI — listed, not checked
no DOI — not checkedAkanbi, M.A., Okunuga, S.A., Sofoluwe, A.B.: Step Size Bounds for a Class of Multiderivative Explicit Runge-Kutta Methods, Modeling and Simulation in Engineering, Economics and Management, pp 188–197. Springer, Berlin (2012)
no DOI — not checkedButcher, J.C.: The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods. Wiley, Chichester (1987)
no DOI — not checkedGear, C.W.: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs (1971)
no DOI — not checkedHairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I. Nonstiff problems, 2nd edn. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin (1993)
no DOI — not checkedIserles, A.: A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press (1996)
no DOI — not checkedLambert, J.D.: Computational Methods in Ordinary Differential Equations. Wiley, New York (1973)
no DOI — not checkedÖkten Turacı, M., Öziş, T.: A note on explicit three-derivative Runge-Kutta methods (ThDRK). Bull. Internat. Math. Virtual Inst 5(1), 65–72 (2015)
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