Some Numerical Remarks on a Meshless Approximation Method

2016 ◽  
Author(s):  
Elisa Francomano ◽  
Giorgio Micale ◽  
Marta Paliaga ◽  
Guido Ala
Keyword(s):  
Approximation Method ◽  
Meshless Approximation

A NEW BACKUS–GILBERT MESHLESS APPROXIMATION METHOD FOR INITIAL-BOUNDARY VALUE PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 03 (03) ◽  
pp. 337-353 ◽  
Author(s):  
CHRISTOPHER D. BLAKELY
Keyword(s):  
Boundary Value Problems ◽  
Approximation Method ◽  
Burgers Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Two Dimensions ◽  
Initial Boundary Value Problems ◽  
Meshless Collocation ◽  
Meshless Approximation ◽  
Initial Boundary Value

A Backus–Gilbert approximation method is introduced in this paper as a tool for numerically solving initial-boundary value problems. The formulation of the method with its connection to the standard moving least-squares formulation will be given along with some numerical examples including a numerical solution to the viscous nonlinear Burgers equation in two-dimensions. In addition, we highlight some of the main advantages of the method over previous numerical methods based on meshless collocation approximation in order to validate its robust approximating power and easy handling of initial-boundary value problems.

scholarly journals Meshless approximation method of one-dimensional oscillatory Fredholm integral equations

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 861-877
Author(s):  
Z Zaheer-Ud-Din ◽  
S Siraj-Ul-Islam
Keyword(s):  
Integral Equation ◽  
Approximation Method ◽  
Meshless Method ◽  
Cost Effective ◽  
Solution Algorithm ◽  
Fredholm Integral Equations ◽  
Local Approach ◽  
One Dimensional ◽  
Multidimensional Geometry ◽  
Meshless Approximation

In this findings, a numerical meshless solution algorithm for 1D oscillatory Fredholm integral equation (OFIE) is put forward. The proposed algorithm is based on Levin?s quadrature theory (LQT) incorporating multi-quadric radial basis function (MQ-RBF). The procedure involves local approach of MQ-RBF differentiation matrix. The proposed method is specially designed to handle the case when the kernel function (KF) involves stationary point(s) (SP(s)). In addition to that, the model without SP(s) is also considered. The main advantage of the meshless procedure is that it can be easily extended to multidimensional geometry. These models have several physical applications in the area of engineering and sciences. The existence of the SP(s) in such models has numerous applications in the field of scattering and acoustics etc. (see [1, 2, 4, 6-8]). The proposed meshless method is accurate and cost-effective and provides a trustworthy platform to solve OFIE(s).

Using the Combination of GM(1,1) and Taylor Approximation Method to Predict the Academic Achievement of Student

2014 ◽  
Vol 1 (2) ◽  
pp. 55-69 ◽  
Author(s):  
Phuoc-Hai Nguyen ◽  
◽  
Tian-Wei Sheu ◽  
Phung-Tuyen Nguyen ◽  
Duc-Hieu Pham ◽  
...  
Keyword(s):  
Academic Achievement ◽  
Approximation Method ◽  
Taylor Approximation

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

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