Analysis and Improved Methods for the Error Estimation of Numerical Solutions in Solid and Multibody Dynamics

2007 ◽  
pp. 69-89
Author(s):  
Ignacio Romero ◽  
Luis M. Lacoma
Keyword(s):  
Error Estimation ◽  
Multibody Dynamics ◽  
Numerical Solutions ◽  
Improved Methods

scholarly journals Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mingxu Yi ◽  
Kangwen Sun ◽  
Jun Huang ◽  
Lifeng Wang
Keyword(s):  
Numerical Method ◽  
Error Estimation ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Approximation Solution ◽  
Cas Wavelets

A numerical method based on the CAS wavelets is presented for the fractional integrodifferential equations of Bratu type. The CAS wavelets operational matrix of fractional order integration is derived. A truncated CAS wavelets series together with this operational matrix is utilized to reduce the fractional integrodifferential equations to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited2k(2M+1). The convergence and error estimation of CAS wavelets are also given. Two examples are included to demonstrate the validity and applicability of the approach.

scholarly journals Numerical methods for the multiplicative partial differential equations

2017 ◽  
Vol 15 (1) ◽  
pp. 1344-1350
Author(s):  
Muhammet Yazıcı ◽  
Harun Selvitopi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Methods ◽  
Error Estimation ◽  
Truncation Error ◽  
Numerical Solutions ◽  
Partial Differential ◽  
The Matrix ◽  
The Stability ◽  
Truncation Error Estimation

Abstract We propose the multiplicative explicit Euler, multiplicative implicit Euler, and multiplicative Crank-Nicolson algorithms for the numerical solutions of the multiplicative partial differential equation. We also consider the truncation error estimation for the numerical methods. The stability of the algorithms is analyzed by using the matrix form. The result reveals that the proposed numerical methods are effective and convenient.

ADAPTIVE MESHFREE METHOD BASED ON ADDING AND MOVING NODES

2006 ◽  
Vol 03 (04) ◽  
pp. 429-443 ◽  
Author(s):  
SEIYA HAGIHARA ◽  
SHINJI MOTODA ◽  
MITSUYOSHI TSUNORI ◽  
TORU IKEDA ◽  
NORIYUKI MIYAZAKI
Keyword(s):  
Error Estimation ◽  
Basis Function ◽  
Numerical Solutions ◽  
Infinite Plate ◽  
Meshfree Method ◽  
Threshold Value ◽  
Posteriori Error ◽  
Quadrature Point ◽  
Analysis Model ◽  
Adaptive Analysis

The objective of the present research is to apply element-free Galerkin (EFG) method to adaptive analyses. It is necessary to estimate error of numerical solutions of EFG method for adaptive analyses to evaluate accuracy of EFG method. Posteriori errors can be estimated by differences of solutions between the linear and the quadratic basis functions. But it is not economical to perform the two respective calculations in regard to the linear and the quadratic basis function. Then the linear function is used only when the stiffness matrix is calculated. Then both the linear and the quadratic basis function are used when the stress and strain are calculated. The error estimation is performed in an each background cell by using the error of energy norm. In the adaptive analysis, a node is added at the quadrature point which is the same as the center of gravity of a background cell where the error is higher than the threshold value. The nodal relocation method is applied to smoothing the distribution of nodes in domain of an analysis model. The nodal relocation method in which nodes are automatically moved and relocated using physical interbubble forces called bubble meshing for FEM is applied to the adaptive analysis after additional nodes are generated. The nodes are relocated corresponding to the error of the background cells. The calculations of the analysis can be repeated again after the posteriori error estimation. The adaptive EFG method and the nodal relocation method are applied to a problem of an infinite plate with a hole subjected to a uniform tension. Nodal density is increased at the vicinity of the hole where the error is large in the analysis. The nodal relocation method can be successful to relocate the nodes which are generated at the quadrature points of higher posteriori error. The difference between the calculated solution and the exact solution are smaller than that of the previous solution as the calculations are repeated.

scholarly journals Robust control of PGD-based numerical simulations

2012 ◽  
Author(s):  
Ludovic Chamoin ◽  
Pierre Ladevèze
Keyword(s):  
Robust Control ◽  
Numerical Simulations ◽  
Error Estimation ◽  
Constitutive Relation ◽  
Numerical Solutions ◽  
Error Estimator ◽  
Error Sources ◽  
Adaptive Procedures ◽  
Constitutive Relation Error

In this paper, we develop an error estimator that enables to control effectively the quality of numerical solutions obtained using proper generalised decomposition. The method is based on the Constitutive Relation Error and the construction of associated admissible fields. It takes all error sources (discretisations, truncation of the modal representation, etc.) into account and can be used, introducing adjoint-based techniques, for goal-oriented error estimation. Furthermore, specific indicators can be derived to split error contributions and thus drive adaptive procedures in an optimal manner.

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