Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method

2007 ◽  
Vol 31 (7) ◽  
pp. 614-623 ◽  
Author(s):  
C.-S. Huang ◽  
C.-F. Lee ◽  
A.H.-D. Cheng
Keyword(s):  
Error Estimate ◽  
Collocation Method ◽  
High Precision ◽  
Shape Factor ◽  
Optimal Shape

Generalized Multiquadrics with Optimal Shape Parameter and Exponent for Deflection and Stress of Functionally Graded Plates

2014 ◽  
Vol 709 ◽  
pp. 121-124 ◽  
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao
Keyword(s):  
Genetic Algorithm ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Shape Parameter ◽  
Optimal Shape ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Radial Basis ◽  
Meshless Collocation

Deflection and stress of simply functionally graded plates are calculated by the meshless collocation method based on generalized multiquadrics radial basis function. The generalized multiquadric radial basis function has the shape parameter c and exponent which have the important effect in the accuracy of the approximation. The deflection and stress of simply functionally graded plates are calculated using the generalized multiquadrics with optimal shape parameter and exponent which is optimized by the genetic algorithm.

scholarly journals On the approximate solution of the boundary value problem for the Helmholtz equation with impedance condition

2019 ◽  
Vol 488 (3) ◽  
pp. 233-236
Author(s):  
A. R. Aliev ◽  
R. J. Heydarov
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Error Estimate ◽  
Helmholtz Equation ◽  
Collocation Method ◽  
Boundary Value ◽  
Impedance Boundary ◽  
Impedance Condition

In this work, we present a justification of collocation method for integral equation of the impedance boundary value problem for the Helmholtz equation. We also build a sequence which converges to the exact solution of our problem and we obtain an error estimate.

scholarly journals Chebyshev Collocation Method for Parabolic Partial Integrodifferential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
M. Sameeh ◽  
A. Elsaid
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Error Estimate ◽  
Collocation Method ◽  
Integrodifferential Equation ◽  
Chebyshev Polynomials ◽  
Difference Method ◽  
A Priori ◽  
Chebyshev Collocation Method ◽  
Partial Integrodifferential Equation

An efficient technique for solving parabolic partial integrodifferential equation is presented. This technique is based on Chebyshev polynomials and finite difference method.A priorierror estimate for the proposed technique is deduced. Some examples are presented to illustrate the validity and efficiency of the presented method.

scholarly journals Numerical solution of a class of advection-reaction-diffusion system

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1503-1511
Author(s):  
Li Cao ◽  
Zhanxin Ma
Keyword(s):  
Numerical Experiment ◽  
Numerical Solution ◽  
Collocation Method ◽  
High Precision ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Collocation Methods ◽  
Barycentric Interpolation ◽  
Precision Method

In this article, the barycentric interpolation collocation methods is proposed for solving a class of non-linear advection-reaction-diffusion system. Compared with other methods, the numerical experiment shows the barycentric interpolation collocation method is a high precision method to solve the advection- reaction-diffusion system.

scholarly journals An Asymptotic Expansion for the Error Term in the Brent-McMillan Algorithm for Euler’s Constant

2019 ◽  
Vol 11 (3) ◽  
pp. 60
Author(s):  
R. B. Paris
Keyword(s):  
Asymptotic Expansion ◽  
Positive Integer ◽  
Error Estimate ◽  
High Precision ◽  
Error Term ◽  
Bessel Functions ◽  
Modified Bessel Functions ◽  
Optimal Error ◽  
Precise Information ◽  
Large Positive Integer

The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler’s constant γ and is based on the modified Bessel functions I_0(2x) and K_0(2x). An error estimate for this algorithm relies on the optimally truncated asymptotic expansion for the product I_0(2x)K_0(2x) when x assumes large positive integer values. An asymptotic expansion for this optimal error term is derived by exploiting the techniques developed in hyperasymptotics, thereby enabling more precise information on the error term than recently obtained bounds and estimates.

Optimal Shape Adjustment of Large High-Precision Cable Network Structures

AIAA Journal ◽  
2021 ◽  
Vol 59 (4) ◽  
pp. 1441-1456
Author(s):  
Sichen Yuan ◽  
Wuming Jing
Keyword(s):  
High Precision ◽  
Optimal Shape ◽  
Network Structures ◽  
Cable Network ◽  
Shape Adjustment
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