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Stochastic differential equations (SDEs) represent physical phenomena dominated by stochastic processes. Similar to deterministic ordinary differential equations (ODEs), various numerical schemes are proposed for SDEs. Stability analysis is significant for numerical SDEs as well, however a few results have been known. We have proposed the mean-square(More)
Bounds of the matrix eigenvalues and its exponential by Lyapunov equation Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and(More)
Numerical stability is considered for several Runge-Kutta methods to systems of neutral delay differential equations. The linear stability analysis is adopted to the system. Adapted with the equistage interpolation process as well as the continuous extension, the Runge-Kutta methods are shown to have the numerical stability similar to the analytical(More)
We study the solitary waves and their interaction for a six-order generalized Boussinesq equation (SGBE) both numerically and analytically. A shooting method with appropriate initial conditions, based on the phase plane analysis around the equilibrium point, is used to construct the solitary-wave solutions for this nonintegrable equation. A symmetric(More)
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