CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

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SHAMOOSHAKY M.M.; ASSARI P.; ADIBI H.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Paper Information

Journal: INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION Year:2014 | Volume:4 | Issue:4 Page(s): 377-387

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Title

CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

Author(s)

SHAMOOSHAKY M.M. | ASSARI P. | ADIBI H. | Issue Writer Certificate

Keywords

BOUNDARY INTEGRAL EQUATION

LOGARITHMIC SINGULAR KERNEL

GALERKIN METHOD

CAS WAVELET

LAPLACE'S EQUATION

SPARSE MATRIX

Abstract

In this paper, we present a computational method for solving BOUNDARY INTEGRAL EQUATIONs with LOGARITHMIC SINGULAR KERNELs which occur as reformulations of a boundary value problem for LAPLACE'S EQUATION. The method is based on the use of the GALERKIN METHOD with CAS WAVELETs constructed on the unit interval as basis. This approach utilizes the non- uniform Gauss-Legendre quadrature rule for approximating logarithm-like singular integrals and so reduces the solution of BOUNDARY INTEGRAL EQUATIONs to the solution of linear systems of algebraic equations. The properties of CAS WAVELETs are used to make the wavelet coefficient matrices sparse, which eventually leads to the sparsity of the coefficient matrix of the obtained system. Finally, the validity and efficiency of the new technique are demonstrated through a numerical example.

Cites

A STRONG COMPUTATIONAL METHOD FOR SOLVING OF SYSTEM OF INFINITE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS

References

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APA: Copy

SHAMOOSHAKY, M.M., ASSARI, P., & ADIBI, H.. (2014). CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, 4(4), 377-387. SID. https://sid.ir/paper/328312/en

Vancouver: Copy

SHAMOOSHAKY M.M., ASSARI P., ADIBI H.. CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION[Internet]. 2014;4(4):377-387. Available from: https://sid.ir/paper/328312/en

IEEE: Copy

M.M. SHAMOOSHAKY, P. ASSARI, and H. ADIBI, “CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS,” INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, vol. 4, no. 4, pp. 377–387, 2014, [Online]. Available: https://sid.ir/paper/328312/en

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