A new kind of numerical method based on rational spectral collocation with the sinh transformation is presented for solving parameterized singularly perturbed two-point boundary value problems with one boundary layer. By means of the sinh transformation, the original Chebyshev points are mapped onto the transformed ones clustered near the singular points of the problem. The results from asympto...

this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by ...

The Large Deviation Principle is derived for several unbounded additive functionals of centered stationary Gaussian processes. For example, the rate function corresponding to 1 T ∫ T 0 X t dt is the Fenchel-Legendre transform of L(y) = − 1 4π ∫∞ −∞ log(1−4πyf(s))ds, where Xt is a continuous time process with the bounded spectral density f(s). Similar results in the discrete-time version are obt...

In this paper, we introduce the dissipative spectral methods (DSM) for the first order linear hyperbolic equations in one dimension. Specifically, we consider the Fourier DSM for periodic problems and the Legendre DSM for equations with the Dirichlet boundary condition. The error estimates of the methods are shown to be quasioptimal for variable-coefficients equations. Numerical results are giv...

We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of “Slinky” inf...