Results 21 to 30 of about 13,068 (272)
Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
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Computers & Mathematics with Applications, 1987 It is shown how the embedded Runge-Kutta-Nyström (RKN) process for the numerical solution of a special second-order initial value problem can be extended by the addition of a so-called dense output formulae for the dependent variable and its derivative. It results in RKN triples yielding non-mesh point solutions and thereby enhancing the practicability
Dormand, J.R., Prince, P.J.
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Propagators for the Time-Dependent Kohn-Sham Equations: Multistep, Runge-Kutta, Exponential Runge-Kutta, and Commutator Free Magnus Methods. [PDF]
Journal of Chemical Theory and Computation, 2018 We examine various integration schemes for the time-dependent Kohn-Sham equations. Contrary to the time-dependent Schrödinger's equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density.
Adrián Gómez Pueyo +3 more
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Extrapolated Implicit–Explicit Runge–Kutta Methods
Mathematical Modelling and Analysis, 2014 We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by
Angelamaria Cardone +3 more
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Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means
Kubik, 2020 This paper discuss how to modified Fourth order Runge-Kutta Kutta method based on the geometric mean. Then we have parameters and however by re-comparing the Taylor series expansion of and up to the 4th order. For make error term re-compering
Irma Suryani +3 more
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Strong approximation for Itô stochastic differential equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2015 In this paper, a class of semi-implicit two-stage stochastic Runge-Kutta methods (SRKs) of strong global order one, with minimum principal error constants are given.
Mehran Namjoo
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Continuous-Stage Runge–Kutta Approximation to Differential Problems
Axioms, 2022 In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge–Kutta methods named Hamiltonian Boundary Value Methods (HBVMs).
Pierluigi Amodio +2 more
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Practical symplectic partitioned Runge–Kutta and Runge–Kutta–Nyström methods
Journal of Computational and Applied Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Blanes, S., Moan, P. C.
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SIAM Journal on Scientific Computing, 2019 The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is extended to general
Hendrik Ranocha +4 more
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Applied Mathematics Letters, 2020 We utilize the invariant energy quadratization approach to transform the nonlinear Hamiltonian ODE into an equivalent form which has a quadratic energy. Then the reformulation is discretized using a class of diagonally implicit Runge–Kutta schemes.
Hong Zhang, Xu Qian, Songhe Song
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