In this paper we re-examine the Geske-Johnson formula (1984) and extend the analysis by deriving a modified Geske-Johnson formula that can overcome the possibility of non-uniform convergence encountered in the original Geske-Johnson formula. Furthermore, we propose a numerical method, the repeated Richardson extrapolation, which is able to estimate the interval of true option values when the ac...

in this paper, mixed convection of al2o3-eg-water nanofluid in a square lid-driven enclosure is investigated numerically. the focus of this study is on the effects of variable thermophysical properties of the nanofluid on the heat transfer characteristics. the top moving and the bottom stationary horizontal walls are insulated, while the vertical walls are kept at different constant temperature...

Recently, we derived some new numerical quadrature formulas of trapezoidal rule type for the integrals I (1)[g] = ∫ b a g(x) x−t dx and I (2)[g] = ∫ b a g(x) (x−t)2 dx . These integrals are not defined in the regular sense; I (1)[g] is defined in the sense ofCauchy PrincipalValuewhile I (2)[g] is defined in the sense of Hadamard Finite Part. With h = (b − a)/n, n = 1, 2, . . ., and t = a+kh for...

This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in RN , N ≥ 2. The main feature of the approach is that it does not rely on a traditional asymptotic error expansion, but rather depends on a more easily proved weaker a p...

We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson...

Problem 1 (Convergence of Richardson iteration). This method’s operator has the form T = I − BA = I − ωA because B = ωI. The eigenvectors of T are – as is easy to verify, the same as those of A, and the eigenvalues of T are λi(T ) = 1− ωλi(A). To prove that the method converges, it is convenient to verify that the l2 norm of T is less than one because we can then express everything in terms of ...

the effects of single walled carbon nanotube (swcnt) on mixed convection in a cavity are investigated numerically. the problem is studied for different richardson numbers (0.1-10), volume fractions of nanotubes (0-1%), and aspect ratio of the cavity (0.5-2.5) when the grashof number is equal to 103. the volume fraction of added nanotubes to water as base fluid are lowers than 1% to make dilute ...

Many problems in modern nancial economics involve the solution of continuous-time, continuous-state stochastic control problems. Since explicit solutions of such problems are extremely rare, e cient numerical methods are called for. The Markov chain approximation approach provides a class of methods that are simple to understand and implement. In this paper, we compare the performance of di ere...

The stability of a large class of nonlinear sequence transformations is analyzed. of the convergence behavior of the J transformation. Similar to recent results of Sidi, it is proved that the pJ transformations , the Weniger S transformation, the Levin transformation and a special case of the Generalized Richardson Extrapolation Process of Sidi are S-stable. An eecient algorithm for the calcula...

Monotonicity of one or more derivatives of the integrand is shown to imply a corresponding property of the approximating Romberg scheme. This is of importance in connection with error estimation by majorants [6]. The monotonicity properties are derived from an elementary study of the kernel functions involved. A possible explanation is given of the monotonicity which frequently occurs in applic...