Investigation of the Numerical Solution of Integral Equation with Kernels Involving Logarithmic Functions

The main aim of this paper is to investigate the numerical solution of first kind integral equation of logarithmic kernel when using spectral method. Our approach consists of limiting the boundary to the unit interval and specify a logarithmic kernel. The behavior of the solution on the unit interval was analyzed and the advantages and disadvantages of this approach was shown.

[1]  Khosrow Maleknejad,et al.  The collocation method for Hammerstein equations by Daubechies wavelets , 2006, Appl. Math. Comput..

[2]  Simon N. Chandler-Wilde,et al.  Numerical conformal mapping via Chebyshev weighted solutions of Symm's integral equation , 1993 .

[3]  M. A. Jaswon,et al.  Integral equation methods in potential theory and elastostatics , 1977 .

[4]  J. Littlewood,et al.  Some new properties of fourier constants , 1927 .

[5]  M. A. Jaswon.  Boundary Integral Equations , 1984 .

[6]  B. Samet,et al.  Q-INTEGRAL EQUATIONS OF FRACTIONAL ORDERS , 2016 .

[7]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[8]  T. A. Zang,et al.  Spectral Methods: Fundamentals in Single Domains , 2010 .

[9]  Carlos Alberto Brebbia.  Boundary element techniques in computer aided engineering , 1984 .

[10]  A. Jafarian,et al.  A Numerical Method for Solving Nonlinear Integral Equations in the Urysohn Form , 2013 .

[11]  Bengt Fornberg,et al.  A practical guide to pseudospectral methods: Introduction , 1996 .

[12]  Carlos Alberto Brebbia,et al.  Topics in Boundary Element Research , 1985 .

[13]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .

[14]  Carlos Alberto Brebbia.  New Developments in Boundary Element Methods , 1978 .

[15]  Emil Sobhy Saad Shokrallah,et al.  Page 1 Modified Iterative Method For the Solution of Fredholm Integral Equations of the Second Kind via Matrices , 2015 .

[16]  Andrew H. Van Tuyl,et al.  Acceleration of convergence of a family of logarithmically convergent sequences , 1994 .

[17]  Thorsten Gerber,et al.  Handbook Of Mathematical Functions , 2016 .