A novel collocation method for a coupled system of singularly perturbed linear equations is presented. This method is based on rational spectral collocation method in barycentric form with sinh transform. By sinh transform, the original Chebyshev points are mapped into the transformed ones clustered near the singular points of the solution. The results from asymptotic analysis about the singula...

The double exponential (DE) formulas for numerical integration are known to be highly efficient, more efficient than the single exponential (SE) formulas in many cases. Function classes suited to the SE formulas have already been investigated in the literature through rigorous mathematical analysis, whereas this is not the case with the DE formulas. This paper identifies function classes suited...

I show that the potential V (x,m) = [b 4 −m(1−m)a(a+ 1) ] sn(x,m) dn(x,m) − b(a+ 1 2 ) cn(x,m) dn(x,m) constitutes a QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+ 1 band edge eigenvalues and eigenfunctions can be obtained analytically. In the limit of m going to 0 or 1, I recover the well known results for the QES doubl...

The model for α = 1, β = 1/(m + 1) and γ = 0 was studied by Bagolubasky and Clarkson et al. A second model for α = 0, β = −(1/2) and γ = 0 was studied by Parker and solitary wave solutions were obtained as well. However, a third model was investigated in Refs. 10 and 11 for m = 1 and m = 2 where explicit solitary wave solutions and kinks solutions were derived. For m ≥ 1, we get consecutive exp...

I show that the potential V (x,m) = [b 4 −m(1−m)a(a+ 1) ] sn(x,m) dn(x,m) − b(a+ 1 2 ) cn(x,m) dn(x,m) constitutes an unusual QES band-structure problem in one dimension. In particular, I show that for any positive integral or half-integral a, 2a+ 1 band edge eigenvalues and eigenfunctions can be obtained analytically. However, the associated orthogonal polynomials satisfy fourterm (rather than...

We obtain the large-n asymptotics of the partition function Zn of the six-vertex model with domain wall boundary conditions in the antiferroelectric phase region, with the weights a D sinh. t/, b D sinh. C t/, c D sinh.2 /, jt j < . We prove the conjecture of Zinn-Justin, that as n ! 1, Zn D C#4.n!/F n Œ1 C O.n 1/ , where ! and F are given by explicit expressions in and t , and #4. ́/ is the Jac...

in this paper, following the methods of connor, we introduce some new generalized double difference sequencespaces using summability with respect to a two valued measure, double infinite matrix and an orlicz function in 2-normed spaces which have unique non-linear structure and examine some of their properties.