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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Hamiltonian System With An Even Term, Gregory S. Spradlin
A Hamiltonian System With An Even Term, Gregory S. Spradlin
Gregory S. Spradlin
No abstract provided.
An Augmented Galerkin Method For Singular Integral Equations With Hilbert Kernel, S. Abbasbandy, E. Babolian
An Augmented Galerkin Method For Singular Integral Equations With Hilbert Kernel, S. Abbasbandy, E. Babolian
Saeid Abbasbandy
In recent papers, Delves [2] and others [1], [3] described a Chebyshev series method for the numerical solution of integral equations with non-singular kernels or some particular singular kernels, for example Green's function kernel, logarithmic and Cauchy kernels and so on. In this paper we describe a Fourier series expansion method for a class of singular integral equations with Hilbert kernel and constant coefficients. We give a number of numerical examples showing that Galerkin method works well in practice.
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Lyapunov Exponents Of Linear Stochastic Functional-Differential Equations. Ii. Examples And Case Studies, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow
Articles and Preprints
We give several examples and examine case studies of linear stochastic functional differential equations. The examples fall into two broad classes: regular and singular, according to whether an underlying stochastic semi-flow exists or not. In the singular case, we obtain upper and lower bounds on the maximal exponential growth rate $\overlineλ1$(σ) of the trajectories expressed in terms of the noise variance σ . Roughly speaking we show that for small σ, $\overlineλ1$(σ) behaves like -σ2 /2, while for large σ, it grows like logσ. In the regular case, it is shown that a discrete Oseledec …