scholarly journals Error analysis of the Tau method: dependence of the approximation error on the choice of perturbation term

1993 ◽  
Vol 25 (1) ◽  
pp. 89-104 ◽  
Author(s):  
S. Namasivayam ◽  
E.L. Ortiz
Keyword(s):  
Error Analysis ◽  
Approximation Error ◽  
Tau Method ◽  
Perturbation Term

scholarly journals An integral equation formulation of the N-body dielectric spheres problem. Part 1: Numerical analysis

2020 ◽  
Author(s):  
Muhammad Hassan ◽  
Benjamin Stamm
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Error Analysis ◽  
Convergence Rates ◽  
A Priori ◽  
Approximation Error ◽  
Spherical Particles ◽  
Integral Equation Formulation ◽  
Dielectric Spheres ◽  
The Stability

In this article, we analyse an integral equation of the second kind that represents the solution of N interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the stability constants- and thus the approximation error- with respect to the number N of involved dielectric spheres. We develop a new a priori error analysis that demonstrates N-independent stability of the continuous and discrete formulations of the integral equation. Consequently, we obtain convergence rates that are independent of N.

scholarly journals Approximate conversion of Bézier curves

1995 ◽  
Vol 51 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Yungeom Park ◽  
U Jin Choi ◽  
Ha-Jine Kimn
Keyword(s):  
Error Analysis ◽  
A Priori ◽  
Approximation Error ◽  
Bézier Curve ◽  
Bezier Curve ◽  
A Priori Bounds ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Geometric Properties

The methods for generating a polynomial Bézier approximation of degree n − 1 to an nth degree Bézier curve, and error analysis, are presented. The methods are based on observations of the geometric properties of Bézier curves. The approximation agrees at the two endpoints up to a preselected smoothness order. The methods allow a detailed error analysis, providing a priori bounds of the point-wise approximation error. The error analysis for other authors’ methods is also presented.

scholarly journals Approximation Error Analysis of Some Deep Backward Schemes for Nonlinear PDEs

2022 ◽  
Vol 44 (1) ◽  
pp. A28-A56
Author(s):  
Maximilien Germain ◽  
Huyên Pham ◽  
Xavier Warin
Keyword(s):  
Error Analysis ◽  
Approximation Error ◽  
Nonlinear Pdes

scholarly journals A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
E. Tohidi ◽  
Kh. Erfani ◽  
M. Gachpazan ◽  
S. Shateyi
Keyword(s):  
Error Analysis ◽  
Operational Matrix ◽  
Numerical Approach ◽  
Bernoulli Polynomial ◽  
Tau Method ◽  
Algebraic Equations ◽  
Fundamental Structure ◽  
Polynomial Approximations ◽  
Mild Conditions ◽  
Operational Matrix Of Differentiation

A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation. The fundamental structure of the presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13.

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