Implicit Runge-Kutta-Nyström methods for general second-order Volterra integro-differential equations

Computers & Mathematics with Applications ◽

10.1016/0898-1221(87)90050-2 ◽

1987 ◽

Vol 14 (7) ◽

pp. 549-559 ◽

Author(s):

H. Brunner

Keyword(s):

Differential Equations ◽

Second Order ◽

Nyström Methods ◽

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Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations

Numerical Algorithms ◽

10.1007/s11075-015-9979-4 ◽

2015 ◽

Vol 70 (4) ◽

pp. 897-927 ◽

Author(s):

Zhaoxia Chen ◽

Zeyu Qiu ◽

Juan Li ◽

Xiong You

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Nyström Methods ◽

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An improved class of generalized Runge–Kutta–Nyström methods for special second-order differential equations

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/s1007-5704(03)00111-4 ◽

2004 ◽

Vol 9 (2) ◽

pp. 217-227 ◽

Author(s):

Jorge Alvarez ◽

Jesús Rojo

Keyword(s):

Differential Equations ◽

Second Order ◽

Second Order Differential Equations ◽

Nyström Methods ◽

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Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.03.006 ◽

2019 ◽

Vol 142 ◽

pp. 171-189

Author(s):

Zhaoxia Chen ◽

Lei Shi ◽

Siyao Liu ◽

Xiong You

Keyword(s):

Differential Equations ◽

Second Order ◽

Nyström Methods ◽

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Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise

Advances in Difference Equations ◽

10.1186/s13662-019-2133-1 ◽

2019 ◽

Vol 2019 (1) ◽

Author(s):

Qiang Ma ◽

Yuanwei Song ◽

Wei Xiao ◽

Wendi Qin ◽

Xiaohua Ding

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Multiplicative Noise ◽

Second Order ◽

Structure Preserving ◽

Nyström Methods ◽

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Two-sided Runge-Kutta method accurate to sixth order for second-order ordinary differential equations

Journal of Mathematical Sciences ◽

10.1007/bf01250583 ◽

1994 ◽

Vol 69 (6) ◽

pp. 1404-1409

Author(s):

N. S. Golovan’ ◽

N. Ya. Lyashchenko

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Sixth Order ◽

Kutta Method ◽

Runge Kutta Method ◽

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New explicit stabilized stochastic Runge-Kutta methods with weak second order for stiff Itô stochastic differential equations

Numerical Algorithms ◽

10.1007/s11075-018-0615-y ◽

2018 ◽

Vol 82 (2) ◽

pp. 593-604

Author(s):

Xiao Tang ◽

Aiguo Xiao

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Second Order ◽

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Optimal time order when implicit Runge–Kutta–Nyström methods solve linear partial differential equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2007.01.001 ◽

2008 ◽

Vol 58 (5) ◽

pp. 539-562 ◽

Author(s):

I. Alonso-Mallo ◽

B. Cano ◽

M.J. Moreta

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Optimal Time ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Nyström Methods ◽

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Runge–Kutta (–Nyström) Methods for Oscillatory Differential Equations

Structure-Preserving Algorithms for Oscillatory Differential Equations ◽

10.1007/978-3-642-35338-3_1 ◽

2013 ◽

pp. 1-25

Author(s):

Xinyuan Wu ◽

Xiong You ◽

Bin Wang

Keyword(s):

Differential Equations ◽

Nyström Methods ◽

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Order reduction and how to avoid it when explicit Runge–Kutta–Nyström methods are used to solve linear partial differential equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2004.07.021 ◽

2005 ◽

Vol 176 (2) ◽

pp. 293-318 ◽

Author(s):

I. Alonso-Mallo ◽

B. Cano ◽

M.J. Moreta

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Order Reduction ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Nyström Methods ◽

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Parallel-iterated pseudo two-step Runge-Kutta-Nyström methods for nonstiff second-order IVPs

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(02)00136-0 ◽

2002 ◽

Vol 44 (1-2) ◽

pp. 143-155 ◽

Author(s):

N.H. Cong ◽

N.T.H. Minh

Keyword(s):

Second Order ◽

Nyström Methods ◽

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