Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel

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RABBANI MOHSEN; Tabatabai adnani Amir Ali; Tamizkar Mandana

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Journal: MATHEMATICAL SCIENCES Year:2018 | Volume:12 | Issue:1 Page(s): 55-60

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Title

Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel

Author(s)

RABBANI MOHSEN | Tabatabai adnani Amir Ali | Tamizkar Mandana | Issue Writer Certificate

Keywords

Integral equation

Integro-differential equation

Singular kernel

Wavelet bases

Legendre polynomial

Orthonormal

Abstract

In this article, we use an effective coupled technique to solve singular integral equations with logarithmic kernel which it occurs in different branches of sciences such as mathematical physics, mechanics, isotropic elastic, etc. At first, we approximate the singular kernel by choosing suitable mesh points and multi-wavelet bases then, Galerkin method is used for solving integral equations. In addition, for simplification and to achieve to a more accuracy, we convert integral equation with logarithmic kernel to integro-differential equation with weakly singular kernel which is solvable with the proposed method. The numerical results show the high accuracy of the solution.

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APA: Copy

RABBANI, MOHSEN, Tabatabai adnani, Amir Ali, & Tamizkar, Mandana. (2018). Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel. MATHEMATICAL SCIENCES, 12(1), 55-60. SID. https://sid.ir/paper/322718/en

Vancouver: Copy

RABBANI MOHSEN, Tabatabai adnani Amir Ali, Tamizkar Mandana. Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel. MATHEMATICAL SCIENCES[Internet]. 2018;12(1):55-60. Available from: https://sid.ir/paper/322718/en

IEEE: Copy

MOHSEN RABBANI, Amir Ali Tabatabai adnani, and Mandana Tamizkar, “Galerkin multi-wavelet bases and mesh points method to solve integral equation with singular logarithmic kernel,” MATHEMATICAL SCIENCES, vol. 12, no. 1, pp. 55–60, 2018, [Online]. Available: https://sid.ir/paper/322718/en

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