**Title:** Numerical solution of Love’s integral equation using Daubechies scale function

**Montes Taurus J. Pure Appl. Math.** / ISSN: 2687-4814

**Article ID:** MTJPAM-D-21-00079; **Volume 4 / Issue 2 / Year 2022**, Pages 45-59

**Document Type:** Research Paper

**Author(s):** Jyotirmoy Mouley ^{a} , Birendra Nath Mandal ^{b}

^{a}Department of Applied Mathematics, University of Calcutta, Kolkata, India

^{b}Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India

Received: 23 December 2021, Accepted: 9 June 2022, Published: 26 July 2022.

**Corresponding Author:** Jyotirmoy Mouley (Email address: jyoti87.cu.wavelet@gmail.com)

**Full Text:** PDF

**Abstract**

This paper presents an efficient numerical scheme for solving a special type of quasi-singular integral equation attributed to Eric Russel Love. The proposed scheme involves the use of an expansion technique of the unknown function of the integral equation in terms of Daubechies scale function. This integral equation has an immense importance in the field of electrostatics. After obtaining the unknown function *f*(*x*) approximately, numerically the capacity of two parallel coaxial disks of unit radius are calculated for different separating parameter *κ* and the computed results are compared with Nomura-Cook results available in the literature. The potential at any point outside the disks is determined numerically. Also the convergence of the proposed method is established.

**Keywords:** Love’s integral equation, Daubechies scale and wavelet function, capacity, potential

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