# Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 467-477

_{n}} of complex numbers which are sequences of approximants of continued fractions K(a

_{n}/b

_{n}) with |a

_{n}|+1=<|b

_{n}|, and study some of their properties. In particular we give truncation error bounds for such continued fractions.

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 331-340

_{n}

_{+}

_{1}=+/-x

_{n}+/-x

_{n}

_{-}

_{1}. Many of these problems involve nonsmooth dynamics (nondifferentiable invariant measures), making computations hard. Here, however, we consider recurrences with smooth...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 211-236

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 431-441

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 371-385

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 387-397

^{a}θcos

^{b}θJ

_{ν}(λsinθ)J

_{μ}(λsinθ)dθ,where J

_{ν}is the Bessel function of order...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 319-329

_{n}

_{+}

_{1}-y

_{n}+q

_{n}y

_{n}

_{-}

_{τ}=0, where {q

_{n}} is an oscillatory sequence. In this note, we make use of the convexity property of the function xlnx to obtain such a criterion which complements some of the existing results even when {q

_{n}}...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 255-276

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 237-245

_{n}(z)+/-iJ

_{n}

_{+}

_{1}(z) and [J

_{n}

_{+}

_{1}(z)]

^{2}-J

_{n}(z)J

_{n}

_{+}

_{2}(z) play an important role in certain physical applications. At the origin these functions have a zero of multiplicity n (if n>=1) and 2n+2, respectively. We prove that all the zeros that lie in C

_{0}are simple. zebec (Kravanja et al., Comput. Phys...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 247-253

^{3}u=f(t,u),0=<t=<2π, with u

^{(}

^{i}

^{)}(0)=u

^{(}

^{i}

^{)}(2π),i=0,1,2, is studied, where ρ>0 and f is singular at u=0. Under suitable conditions on f, it is proved by employing a priori estimates, perturbation technique and Schauder fixed point theorem that the problem has at least one positive...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 409-429

^{-}

^{λ}

^{f}

^{(}

^{x}

^{,}

^{y}

^{)}dxdyfor a wide class of amplitude functions g(x,y) and 'polynomial' (noninteger powers are permitted) phases f(x,y) possessing an isolated, though possibly degenerate, critical point at the origin. The resulting algebraic expansions valid in a certain...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 341-356

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 399-407

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 461-466

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 277-293

^{1}

^{/}

^{2}order in the energy norm. In the present paper, we will first prove that this scheme actually possesses an -uniform convergence order h|lnh|

^{1}

^{/}...

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 357-369

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 443-459

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 479-482

_{1},

_{2})[c

_{m}

_{n}

_{1}(y

_{m}

_{n})]+ i=1sa

_{i}(m,n)f

_{i}(y

_{m}

_{+}

_{1}

_{,}

_{n},

_{1}(y m

_{n}))=0is investigated. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.

Journal of Computational and Applied Mathematics > 2001 > 132 > 2 > 309-318