Moving least squares collocation method for Volterra integral equations with proportional delay

2017 ◽  
Vol 94 (12) ◽  
pp. 2335-2347 ◽  
Author(s):  
H. Laeli Dastjerdi ◽  
M. Nili Ahmadabadi
Keyword(s):  
Least Squares ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Moving Least Squares ◽  
Proportional Delay ◽  
Least Squares Collocation

Numerical solutions of the GEW equation using MLS collocation method

2017 ◽  
Vol 28 (01) ◽  
pp. 1750011
Author(s):  
Ayşe Gül Kaplan ◽  
Yılmaz Dereli
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Solitary Waves ◽  
Numerical Solutions ◽  
Rates Of Convergence ◽  
Numerical Results ◽  
Moving Least Squares ◽  
Test Problems ◽  
Least Squares Collocation ◽  
Energy And Momentum

In this paper, the generalized equal width wave (GEW) equation is solved by using moving least squares collocation (MLSC) method. To test the accuracy of the method some numerical experiments are presented. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution was known [Formula: see text], [Formula: see text] error norms and pointwise rates of convergence were calculated. Also mass, energy and momentum invariants were calculated for every test problems. Obtained numerical results are compared with some earlier works. It is seen that the method is very efficient and reliable due to obtained numerical results are very satisfactorily. Stability analysis of difference equation was done by applying the moving least squares collocation method for GEW equation.

Application of moving least squares algorithm for solving systems of Volterra integral equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mashallah Matinfar ◽  
Elham Taghizadeh ◽  
Masoumeh Pourabd
Keyword(s):  
Least Squares ◽  
Integral Equations ◽  
Approximation Method ◽  
Variable Coefficients ◽  
Volterra Integral Equations ◽  
Moving Least Squares ◽  
Numerical Examples ◽  
Acceptable Accuracy ◽  
Mls Approximation ◽  
Mls Method

Abstract The numerical method developed in the current paper is based on the moving least squares (MLS) method. To this end, the MLS approximation method has been used, and a program has been made which can solve the system of Volterra integral equations (VIEs) with any number of equations and unknown functions. And then the proposed method is implemented on the system of linear VIEs with variable coefficients. The numerical examples are given that show the acceptable accuracy and efficiency of the proposed scheme.

Chebyshev spectral-collocation method for a class of weakly singular Volterra integral equations with proportional delay

2014 ◽  
Vol 22 (4) ◽  
Author(s):  
Z. Gu ◽  
Y. Chen
Keyword(s):  
Error Analysis ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Spectral Collocation Method ◽  
Proportional Delay ◽  
Spectral Collocation ◽  
Weakly Singular ◽  
Chebyshev Spectral Collocation ◽  
Chebyshev Spectral Collocation Method

Abstract-The main purpose of this paper is to propose the Chebyshev spectral-collocation method for a class of the weakly singular Volterra integral equations (VIEs) with proportional delay. The proposed method also are applicable to a class of the weakly singular VIEs with proportional delay possessing unsmooth solution. To provide a rigorous error analysis for the proposed method, we prove the the uniqueness and smoothness of the solution. The error analysis shows that the numerical errors decay exponentially in the infinity norm and the Chebyshev weighted Hilbert space norms. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence.

scholarly journals The least-squares collocation method in the mechanics of deformable solids

2021 ◽  
Vol 1715 ◽  
pp. 012029
Author(s):  
Sergey Golushko ◽  
Vasily Shapeev ◽  
Vasily Belyaev ◽  
Luka Bryndin ◽  
Artem Boltaev ◽  
...  
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Least Squares Collocation ◽  
Deformable Solids ◽  
Mechanics Of Deformable Solids

Collocation method for Fredholm and Volterra integral equations

Kybernetes ◽  
2013 ◽  
Vol 42 (3) ◽  
pp. 400-412 ◽  
Author(s):  
Jalil Rashidinia ◽  
Zahra Mahmoodi
Keyword(s):  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations
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