This report presents several approaches aimed at reducing the bias and uncertainty of the free energy difference estimates obtained using the thermodynamic integration simulation strategy. The central idea is to utilize interpolation schemes, rather than the often-used trapezoidal rule quadrature, to fit the thermodynamic integration data, and obtain a more accurate and precise estimate of the ...

A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of such methods in the context of rigorous computing (where we need guarantees on the accuracy of the result), and from the complexity point of view. It is well-kn...

We consider the problem of efficiently interpolating an “approximate” black-box polynomial p(x) that is sparse when represented in the Chebyshev basis. Our computations will be in a traditional floating-point environment, and their numerical sensitivity will be investigated. We also consider the related problem of interpolating a sparse linear combination of “approximate” trigonometric function...

Copyright q 2011 M. U. Kalmykov and S. P. Sidorov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Wewill estimate the upper and the lower bounds of the integral ∫1 0 Ω t dμ t , where μ runs over all discrete measures, positive on...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

Kasana and Kumar [5] obtained the (p, q)−growth parameters in terms of Chebyshev and interpolation errors for entire functions on a compact set E of positive transfinite diameter. Rizvi and Nautiyal [9] studied the order and type in terms of these errors for the functions which are not entire. But these results do not give any specific information about the growth of non-entire functions if max...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

Free asymmetric transverse vibration of a polar orthotropic thin annular plate with parabolically varying thickness in radial direction have been computed on the basis of classical plate theory considering both the peripheries of the plate elastically restrained against translation and rotation. The fourth order linear differential equation with variable coefficients governing the motion in the...