Abstract
One-step numerical schemes for RODEs with affine noise are derived. Affine-RODE Taylor schemes for bounded, additive and commutative noise are considered. Derivative-free schemes are presented along with multi-step and Runge-Kutta schemes.
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Notes
- 1.
Strictly speaking a RODE is always nonautonomous since the noise depends explicitly on time. The word autonomous is used here to indicate that the drift and noise coefficients \(f_0\), \(f_1\), \(\ldots \), \(f_m\) do not depend on the time variable.
- 2.
When the context is clear the notation x is used for both scalar and vector.
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© 2017 Springer Nature Singapore Pte Ltd.
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Han, X., Kloeden, P.E. (2017). Numerical Schemes for RODEs with Affine Noise. In: Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling, vol 85. Springer, Singapore. https://doi.org/10.1007/978-981-10-6265-0_11
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DOI: https://doi.org/10.1007/978-981-10-6265-0_11
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6264-3
Online ISBN: 978-981-10-6265-0
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