Results 41 to 50 of about 10,395 (165)
A Note on the Construction of Explicit Symplectic Integrators for Schwarzschild Spacetimes
The Astrophysical Journal, 2022 In recent publications, the construction of explicit symplectic integrators for Schwarzschild- and Kerr-type spacetimes is based on splitting and composition methods for numerical integrations of Hamiltonians or time-transformed Hamiltonians associated ...
Naying Zhou +3 more
doaj +1 more source
Economical Runge-Kutta methods
Rendiconti di Matematica e delle Sue Applicazioni, 1995 This paper deals with explicit Runge-Kutta methods of the type \(y_{n + 1} = y_ n + h \sum^ s_{i = 2} b_ i K^ n_ i\), \(K^ n_ i = f(x_ n + c_ ih, y_ n + ha_{i1} K^{n-1}_ s + h \sum^{i - 1}_{j = 2} a_{ij} K^ n_ j)\), with \(b_ 1 = 0\), \(c_ s = 1\). By using information from the previous step one function evaluation is saved.
Costabile Francesco +2 more
openaire +3 more sources
Alexandria Engineering Journal, 2023 Efficient trigonometrically-fitted explicit two-derivative improved Runge–Kutta-Nystro¨m methods with three stage fifth-order, denoted as TFTDIRKN5 method is derived for direct solving special type of second-order ordinary differential equation in the ...
K.C. Lee +3 more
doaj +1 more source
Solving Linear Boundary Value Problem Using Shooting Continuous Explicit Runge-Kutta Method
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017 In this paper we shall generalize fifth explicit Runge-Kutta Feldberg(ERKF(5)) and Continuous explicit Runge-Kutta (CERK) method using shooting method to solve second order boundary value problem which can be reduced to order one.These methods we ...
Madeha Sh. Yousif, Bushra E. Kashiem
doaj
Coherent Chaotic Communication Using Generalized Runge–Kutta Method
MathematicsComputer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of ...
Ivan Babkin +4 more
doaj +1 more source
Academy Journal of Science and Engineering, 2022 Super Runge-Kutta- Nyström (SRKN) method for direct solution of general third order ordinary differential equations (ODEs) is an extension of the Runge-Kutta- Nyström (RKN) for solution of second ODEs.This paper describe and implement by means of a ...
Zamurat A. Adegboye +2 more
doaj
Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems
Abstract and Applied Analysis, 2013 We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and ...
S. Z. Ahmad +3 more
doaj +1 more source
Journal of Low Frequency Noise, Vibration and Active Control, 2022 Nonlinear vibration arises everywhere in a bistable system. The bistable system has been widely applied in physics, biology, and chemistry. In this article, in order to numerically simulate a class of space fractional-order bistable system, we introduce ...
Haitao Liu +3 more
doaj +1 more source
Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order
The Scientific World Journal, 2014 The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented.
Y. H. Cong, C. X. Jiang
doaj +1 more source
Some notes on summation by parts time integration methods
Results in Applied Mathematics, 2019 Some properties of numerical time integration methods using summation by parts (SBP) operators and simultaneous approximation terms are studied. These schemes can be interpreted as implicit Runge-Kutta methods with desirable stability properties such as ...
Hendrik Ranocha
doaj +1 more source