Papers by Keyword: Error Estimate

Abstract: In this work we present a computational method for for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on Adomian Decom-position Method. Convergence analysis is dependable enough to estimate the maximum absolute truncated error of the Adomian series solution. Numerical example is included to demonstrate the validity and applicability of the method.

Abstract: Black-Scholes equation is the basic equation of option pricing in financial mathematics, it is important to study its numerical solution in financial market. This paper constructs a new kind of high order accuracy numerical algorithm (Three-layer difference scheme) for Black-Scholes equation with payment of dividend. Secondly, it gives the convergence of scheme. Thirdly, the stability and error estimates are analyzed. Finally, the numerical examples show the feasibility and effectiveness of the scheme. The truncation error of Three-layer scheme is little worse than Crank-Nicolson scheme and computational cost is little better than Crank-Nicoslon scheme. Therefore, the scheme is better suitable for applying to calculate the option pricing in the demanding high level of instantaneity.

Abstract: The finite difference method is applied to derive approximate solutions for the elasto-plastic bending of Euler-Bernoulli beam problems. The investigations are restricted to a simple exemplary configuration, i.e. a straight cantilevered beam with constant rectangular cross-section and linear-elastic/ideal-plastic material properties, loaded by a constant distributed load. Only finite difference approximations of second-order accuracy are considered and special emphasis is given to the influence of the load step, the number of layers, and the number of nodes. Based on comparisons with the analytical solution, clear recommendations can be given on the required parameters to obtain a certain accuracy in the numerical approach.

Abstract: A disadvantage of the MLS approximation is that the shape function of this method does not satisfy the property of Kronecker Delta function. Thus developing an interpolating MLS approximation is very important. In this paper, the interpolating moving least-squares (IMLS) method presented by Lancaster and Salkauskas is discussed in detail and a simplified expression of the approximation function of the IMLS method is given. The simpler expression makes it more convenient to use this method. The error estimate of the approximation function also is discussed. And a numerical example is given to confirm the results.

Abstract: In this paper, H1-Galerkin mixed element method is proposed to simulate the nonlinear Parabolic problem. The problem is considered in one dimensional space. and optimal error estimates are also established. In particular, our methods can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition.

Abstract: H1-Galerkin expanded mixed element method are discussed for a class of second-order heat equations. The methods possesses the advantage of mixed finite element while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. H1-Galerkin expanded mixed finite element method for heat equations are described, an optimal order error estimate for the methods is obtained.

Abstract: This paper presents an advanced numerical methodology which aims to improve virtually any metal forming processes. It is based on elastoplastic constitutive equations accounting for non-linear mixed isotropic and kinematic hardening “strongly” coupled with isotropic ductile damage. During simulation of metal forming processes, where large plastic deformations with ductile damage occur, severe mesh distorsion takes place after a finite number of incremental steps. Hence an automatic mesh generation with remeshing capabilities is essential to carry out the finite element analysis. Besides, when damage is taken into account a kill element procedure is needed to eliminate the fully damaged elements in order to simulate the growth of macroscopic cracks. The necessary steps to remesh a damaged structure in finite element simulation of forming processes including damage occurrence (initiation and growth) are given. An important part of this procedure is constituted by geometrical and physical error estimates. The meshing and remeshing procedures are automatic and are implemented in a computational finite element analysis package (ABAQUS/Explicit solver using the Vumat user subroutine). Some numerical results are presented to show the capability of the proposed procedure to predict the damage initiation and growth during the metal forming processes.

Abstract: Approximate Double Circular Arc Interpolated Method which was put forward by author, is different from other circular arc interpolated methods in demanding only the corner between normal directions of each circular arcs at intersection point are less than designated allowed value but not demanding contiguous circular arcs are tangent, and makes the calculating be predigested. In order to estimate error of the method, emulated calculating is carried out, namely the course of curve being obtained by reverse engineering is simulated in this paper. The results show: if space between measure points is about 0.1mm in curve being obtained by reverse engineering, then, the most departure of smoothing results from original curve is 0.552μm for the stated example. Influence of the error on NC machining is quite small, so it can meet the needs of NC machining.