A MESHLESS LOCAL GALERKIN METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MOVING LEAST SQUARES TECHNIQUE

Pouria Assari

doi:10.11948/2019.75

2019 Volume 9 Issue 1

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Pouria Assari. A MESHLESS LOCAL GALERKIN METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MOVING LEAST SQUARES TECHNIQUE[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 75-104. doi: 10.11948/2019.75

Citation:

Pouria Assari. A MESHLESS LOCAL GALERKIN METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MOVING LEAST SQUARES TECHNIQUE[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 75-104. doi: 10.11948/2019.75

A MESHLESS LOCAL GALERKIN METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN INTEGRAL EQUATIONS BASED ON THE MOVING LEAST SQUARES TECHNIQUE

Pouria Assari

Department of Mathematics, Faculty of Sciences, Bu-Ali Sina University, Hamedan 65178, Iran

Author Bio: Email address:passari@basu.ac.ir

Abstract

Abstract

In this paper, a computational scheme is proposed to estimate the solution of one- and two-dimensional Fredholm-Hammerstein integral equations of the second kind. The method approximates the solution using the discrete Galerkin method based on the moving least squares (MLS) approach as a locally weighted least squares polynomial fitting. The discrete Galerkin technique for integral equations results from the numerical integration of all integrals in the system corresponding to the Galerkin method. Since the proposed method is constructed on a set of scattered points, it does not require any background meshes and so we can call it as the meshless local discrete Galerkin method. The implication of the scheme for solving two-dimensional integral equations is independent of the geometry of the domain. The new method is simple, efficient and more flexible for most classes of nonlinear integral equations. The error analysis of the method is provided. The convergence accuracy of the new technique is tested over several Hammerstein integral equations and obtained results confirm the theoretical error estimates.
- Hammerstein integral equation /
- discrete Galerkin method /
- moving least squares (MLS) /
- meshless method /
- error analysis
MSC: 65D10, 45G99, 65G99

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References

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