Filter matrix based on interpolation wavelets for solving Fredholm integral equations |
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| Institution: | 1. Mukesh Patel School of Technology Management and Engineering, Narsee Monjee Institute of Management Studies (Deemed to be University), Mumbai-Agra Road, Shirpur 425405, India;2. Department of Mathematics, Pratap College, Amalner 425401, India;3. Department of Mathematics, Veer Narmad South Gujarat University, Magdulla Road, Surat 395007, India;1. Department of Mathematics, Vaagdevi College of Engineering (Autonomous), Warangal 506005, Telangana State, India;2. Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan;3. Mechanical Engineering Department, School of Science, Engineering and Environment (SEE), University of Salford, Manchester, UK;4. Engineering Mechanics Research, Israfil House, Dickenson Road, Manchester, UK;1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa;2. Faculty of Science and Engineering, Department of Mathematics, University of Swaziland, Kwaluseni, Swaziland;3. DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Pretoria, South Africa;1. Department of Mathematics, VIT University, Vellore 632014, India;2. Mechanical Engineering Department, College of Engineering, King Saud University, P. O. Box 800, Riyadh 11421, Saudi Arabia |
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| Abstract: | The interpolation wavelet is used to solve the Fredholm integral equation of the second kind in this study. Hence, by the extension of interpolation wavelets that −1, 1] is divided to 2N+1 (N ⩾ − 1) subinterval, we have polynomials with a degree less than M + 1 in each new interval. Therefore, by considering the two-scale relation the filter coefficients and filter matrix are used as the proof of theorems. The important point is interpolation wavelets lead to more sparse matrix when we try to solve integral equation by an approximate kernel decomposed to a lower and upper resolution. Using n-time, where (n ⩾ 2), two-scale relation in this method errors of approximate solution as O((2−(N+1))n+1). Also, the filter coefficient simplifies the proof of some theorems and the order of convergence is estimated by numerical errors. |
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