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Zbl 0936.65146
Ren, Yuhe; Zhang, Bo; Qiao, Hong
A simple Taylor-series expansion method for a class of second kind integral equations. (English)
[J] J. Comput. Appl. Math. 110, No.1, 15-24 (1999). ISSN 0377-0427

The authors consider the integral equation $$x(s)- \lambda \int^1_0 k(s,t)x(t) dt= y(s),\quad s\in [0,1],$$ with kernel $k$ either a continuous and (rapidly) decreasing convolution kernel, or containing a weak (algebraic) singularity. Motivated by certain limitations of the Taylor series expansion method proposed in {\it M. Perlmutter} and {\it R. Siegel} [ASME J. Heat Transfer, 85, 55-62 (1963)], they show how the desired Taylor coefficient functions can be found by solving a linear algebraic system which does not involve the use of boundary conditions.\par There is no convergence analysis, and no error estimates are given. Instead, the method is applied to three examples of integral equations with smooth kernels (arising in radiative heat transfer and electrostatics), and a constructed example with weakly singular kernel (where, not surprisingly, the method does not do well near the endpoints of the interval of integration).
[H.Brunner (St.John's)]

MSC 2000:: *65R20 Integral equations (numerical methods)
45B05 Fredholm integral equations
45E10 Integral equations of the convolution type

Keywords: second-kind integral equations; Fredholm integral equation; convolution kernel; Taylor series expansion method; radiative heat transfer; electrostatics; weakly singular kernel

Cited in: Zbl 1190.65195

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