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Numerical Algorithms, ISSN 1017-1398, 11/2018, Volume 79, Issue 3, pp. 787 - 800
Two derivative Runge-Kutta methods are Runge-Kutta methods for problems of the form y ′ = f(y) that include the second derivative y ″ = g(y) = f ′(y)f(y) and... 
Two derivative Runge-Kutta methods | Algorithms | Algebra | Numerical Analysis | Computer Science | Numeric Computing | Theory of Computation | Trigonometrical fitting | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | 2-STEP HYBRID METHODS | STABILITY | International trade | Information science | Analysis | Methods
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 3/2018, Volume 56, Issue 3, pp. 799 - 812
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2019, Volume 42, Issue 6, pp. 1955 - 1966
Two‐derivative Runge‐Kutta methods are Runge‐Kutta methods for problems of the form y′ = f(y) that include the second derivative y′′ = g(y) = f ′(y)f(y) and... 
periodic or oscillatory behavior | trigonometrical fitting | two‐derivative Runge‐Kutta methods | two-derivative Runge-Kutta methods | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | INTEGRATION | STABILITY | INITIAL-VALUE PROBLEMS | Coefficients | Test procedures | Construction methods
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 08/2019, Volume 142, pp. 171 - 189
A new family of modified two-derivative Runge-Kutta-Nyström (TDRKN) methods are proposed for solving initial value problems of second-order oscillatory... 
Two-derivative Runge-Kutta-Nyström method | Nyström tree | Order condition | Periodicity region | B-series | Trigonometrical fitting | Two-derivative Runge-Kutta-Nystrom method | MATHEMATICS, APPLIED | Nystrom tree | SYSTEMS | Analysis | Methods | Differential equations
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2010, Volume 53, Issue 2, pp. 171 - 194
Journal Article
Numerical Algorithms, ISSN 1017-1398, 1/2017, Volume 74, Issue 1, pp. 247 - 265
We introduce an algorithm for a numerical integration of ordinary differential equations in the form of y′ = f(y). We extend the two-derivative Runge-Kutta... 
Algorithms | Algebra | Rooted trees | Numerical Analysis | Computer Science | Numeric Computing | Two-derivative Runge-Kutta methods | Order conditions | Theory of Computation | Multi-derivative Runge-Kutta methods | MATHEMATICS, APPLIED | INTEGRATION METHODS | ORDINARY DIFFERENTIAL-EQUATIONS | Analysis | Methods | Differential equations
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2014, Volume 65, Issue 3, pp. 687 - 703
Journal Article
International Journal of Modern Physics C, ISSN 0129-1831, 10/2013, Volume 24, Issue 10, p. 1350073
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 2011, Volume 61, Issue 10, pp. 1046 - 1058
An extension of general linear methods (GLMs), so-called SGLMs (GLMs with second derivative), was introduced to the case in which second derivatives, as well... 
Runge–Kutta stability | Ordinary differential equation | Two-derivative methods | General linear methods | A-stability | Runge-Kutta stability | MATHEMATICS, APPLIED | STIFF SYSTEMS | CONSTRUCTION | MULTISTAGE INTEGRATION METHODS | ORDINARY DIFFERENTIAL-EQUATIONS | EXPLICIT | Architecture | Methods
Journal Article
Journal of Mathematical Chemistry, ISSN 0259-9791, 1/2014, Volume 52, Issue 1, pp. 240 - 254
Journal Article
Numerical Algorithms, ISSN 1017-1398, 3/2014, Volume 65, Issue 3, pp. 651 - 667
Journal Article
Journal of the Nigerian Mathematical Society, ISSN 0189-8965, 08/2015, Volume 34, Issue 2, pp. 128 - 142
We introduce a new class of implicit two-derivative Runge–Kutta collocation methods designed for the numerical solution of systems of equations and show how... 
System of equations | Block hybrid discrete scheme | Continuous scheme | Two-derivative Runge–Kutta methods
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 02/2020, Volume 43, Issue 3, pp. 1267 - 1277
In this work, we consider two‐derivative Runge‐Kutta methods for the numerical integration of first‐order differential equations with oscillatory solution. We... 
phase lag | two‐derivative Runge‐Kutta methods | amplification error | two-derivative Runge-Kutta methods | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | ORDER INFINITY | LAG | INTEGRATION | PAIRS | Amplification | Numerical integration | Numerical methods | Differential equations
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 11/2018, Volume 2040, Issue 1
In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We compare numerical methods with constant... 
trigonometrically fitted methods | Two Derivative Runge Kutta methods | Numerical methods | Runge-Kutta method | Numerical integration
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 02/2014, Volume 76, pp. 1 - 18
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 07/2018, Volume 1978, Issue 1
In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We construct methods with variable... 
phase lag | amplification error | Two Derivative Runge Kutta methods | Numerical methods | Runge-Kutta method | Numerical integration
Journal Article
AIP Conference Proceedings, ISSN 0094-243X, 07/2017, Volume 1863, Issue 1
In this work we consider Two Derivative Runge-Kutta methods. We present the order conditions after applying simplifying conditions. Two new methods of... 
order conditions | Two Derivative Runge Kutta methods | Two body problem | Runge-Kutta method
Journal Article
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