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1. | School of Mathematics & Physics, Qingdao University of Science & Technology, Qingdao 266061, China |
2. | Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, United Kingdom |
References:
[1] |
J. C. Butcher, Numerical Methods for Ordinary Differential Equations,, 2nd ed., (2008).
doi: 10.1002/9780470753767. |
[2] |
Y. Fang, Y. Song and X. Wu, New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems,, Phys. Lett. A, 372 (2008), 6551.
doi: 10.1016/j.physleta.2008.09.014. |
[3] |
A. B. González, P. Martín and J. M. Farto, A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators,, Numer. Math., 82 (1999), 635.
doi: 10.1007/s002110050434. |
[4] |
E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method,, Acta Numer., 12 (2003), 399.
doi: 10.1017/S0962492902000144. |
[5] |
E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems,, Springer-Verlag, (1993).
|
[6] |
G. H. Hardy and M. Riesz, The general theory of Dirichlet series,, Cambridge Tracts in Mathematics and Mathematical Physics, 18 (1964).
|
[7] |
M. Hochbruck and A. Ostermann, Explicit exponential Runge-Kutta methods for semilineal parabolic problems,, SIAM J. Numer. Anal., 43 (2005), 1069.
doi: 10.1137/040611434. |
[8] |
A. Iserles, A First Course in the Numerical Analysis of Differential Equations,, 2nd ed., (2008).
|
[9] |
A. Iserles, G. P. Ramaswami and M. Sofroniou, Runge-Kutta methods for quadratic ordinary differential equations,, BIT, 38 (1998), 315.
doi: 10.1007/BF02512370. |
[10] |
A. Iserles and G. Söderlind, Global bounds on numerical error for ordinary differential equations,, J. Complexity, 9 (1993), 97.
doi: 10.1006/jcom.1993.1007. |
[11] |
A. Iserles and A. Zanna, Preserving algebraic invariants with Runge-Kutta methods,, J. Comp. Appl. Maths., 125 (2000), 69.
doi: 10.1016/S0377-0427(00)00459-3. |
[12] |
S. Mandelbrojt, Dirichlet Series: Principles and Methods,, D. Reidel Publishing Company, (1972).
|
[13] |
L. Perko, Differential Equations and Dynamical Systems,, 3rd ed., (2001).
|
[14] |
R. C. Robinson, An Introduction to Dynamical Systems: Countinuous and Discrete,, Pearson Prentice Hall, (2004).
|
[15] |
J. M. Sanz-Serna, Runge-Kutta schems for Hamiltonian systems,, BIT, 28 (1988), 877.
doi: 10.1007/BF01954907. |
[16] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,, Springer-Verlag, (1990).
doi: 10.1007/978-3-642-97149-5. |
show all references
References:
[1] |
J. C. Butcher, Numerical Methods for Ordinary Differential Equations,, 2nd ed., (2008).
doi: 10.1002/9780470753767. |
[2] |
Y. Fang, Y. Song and X. Wu, New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems,, Phys. Lett. A, 372 (2008), 6551.
doi: 10.1016/j.physleta.2008.09.014. |
[3] |
A. B. González, P. Martín and J. M. Farto, A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators,, Numer. Math., 82 (1999), 635.
doi: 10.1007/s002110050434. |
[4] |
E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method,, Acta Numer., 12 (2003), 399.
doi: 10.1017/S0962492902000144. |
[5] |
E. Hairer, S. P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems,, Springer-Verlag, (1993).
|
[6] |
G. H. Hardy and M. Riesz, The general theory of Dirichlet series,, Cambridge Tracts in Mathematics and Mathematical Physics, 18 (1964).
|
[7] |
M. Hochbruck and A. Ostermann, Explicit exponential Runge-Kutta methods for semilineal parabolic problems,, SIAM J. Numer. Anal., 43 (2005), 1069.
doi: 10.1137/040611434. |
[8] |
A. Iserles, A First Course in the Numerical Analysis of Differential Equations,, 2nd ed., (2008).
|
[9] |
A. Iserles, G. P. Ramaswami and M. Sofroniou, Runge-Kutta methods for quadratic ordinary differential equations,, BIT, 38 (1998), 315.
doi: 10.1007/BF02512370. |
[10] |
A. Iserles and G. Söderlind, Global bounds on numerical error for ordinary differential equations,, J. Complexity, 9 (1993), 97.
doi: 10.1006/jcom.1993.1007. |
[11] |
A. Iserles and A. Zanna, Preserving algebraic invariants with Runge-Kutta methods,, J. Comp. Appl. Maths., 125 (2000), 69.
doi: 10.1016/S0377-0427(00)00459-3. |
[12] |
S. Mandelbrojt, Dirichlet Series: Principles and Methods,, D. Reidel Publishing Company, (1972).
|
[13] |
L. Perko, Differential Equations and Dynamical Systems,, 3rd ed., (2001).
|
[14] |
R. C. Robinson, An Introduction to Dynamical Systems: Countinuous and Discrete,, Pearson Prentice Hall, (2004).
|
[15] |
J. M. Sanz-Serna, Runge-Kutta schems for Hamiltonian systems,, BIT, 28 (1988), 877.
doi: 10.1007/BF01954907. |
[16] |
F. Verhulst, Nonlinear Differential Equations and Dynamical Systems,, Springer-Verlag, (1990).
doi: 10.1007/978-3-642-97149-5. |
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