In this paper we develop numerical techniques of order 2, 4 and 6 for the solution of a fourth order linear equation. A priori error bound is obtained for the fourth order method to prove the convergence of the finite difference scheme. A sufficient condition guaranteeing the uniqueness of the solution of the boundary value problem is also given. Numerical illustrations are tabulated and result...

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil, no special formulas are needed near th...

There is no doubt that the fourth-order King’s family one of important ones among its counterparts. However, it has two major problems: first calculation first-order derivative; secondly, a linear order convergence in case multiple roots. In to improve these complications, we suggested new iterative methods. The main features our scheme are optimal order, being free from derivatives, and workin...

An improved iterative method of Euler’s type for the simultaneous inclusion of polynomial zeros is considered. To accelerate the convergence of the basic method of fourth order, Carstensen-Petković’s approach [7] using Weierstrass’ correction is applied. It is proved that the R-order of convergence of the improved Euler-like method is (asymptotically) 2 + √ 7 ≈ 4.646 or 5, depending of the type...

Dirac sea corrections for bulk properties of finite nuclei are computed within a self-consistent scheme in the σ-ω model. The valence part is treated in the Hartree approximation whereas the sea contribution is evaluated semiclassically up to fourth order in h̄. Numerically, we find a quick convergence of the semiclassical expansion; the fourth order contributing much less than one percent to th...