Approximate solution of first kind singular integral equation with generalized kernel using Legendre multiwavelets

  • Swaraj Paul
  • M. M. Panja
  • B. N. MandalEmail author


In this study, numerical solution of a class of Cauchy type singular integral equations of the first kind with generalized kernels (CSIEFKGK) is obtained using Legendre multiwavelets (LMW). Instead of using complex function theory, the appropriate weight function of the solution is obtained by applying LMW-based numerical scheme. We evaluate the matrix representation of generalized kernel with and without the weight factor using recurrence relations and some elementary methods. Using the multiscale representation of the integral operator, the equation is converted into a system of linear equations. The numerical solution of CSIEFKGK is obtained by solving this systems. Finally, a number of examples including applications of crack problems are considered to illustrate the efficiency of the method developed here.


Cauchy type singular integral equation of the first kind Generalized kernel Legendre multiwavelets Wavelet Galerkin method Multiscale approximation 

Mathematics Subject Classification

65R20 65D15 65T60 45E05 42C40 



The authors thank the reviewers for his comments and suggestions to revise the paper in the present form. This work is supported by a research grant from SERB(DST), No. SR/S4/MS:821/13.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.Department of MathematicsVisva-BharatiSantiniketanIndia
  2. 2.Physics and Applied Mathematics Unit, Indian Statistical Institute 203KolkataIndia

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