×

Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method. (English) Zbl 1061.65145

Summary: We present a Taylor-series expansion method for a class of Volterra integral equations of second kind with smooth or weakly singular kernels. This method use Taylor-series approximation method for integral equation and transform the integral equation to an \(n\)th order, linear differential equation. Boundary conditions for differential equation produce in easy way. This method gives an approximate simple and closed form solution for integral equation. Some numerical examples to illustrate the accuracy of method.

MSC:

65R20 Numerical methods for integral equations
45D05 Volterra integral equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Atkinson, K. E., The Numerical Solution of Integral Equations of the Second Kind (1997), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0155.47404
[2] Delves, L. M.; Mohamed, J. L., Computational Methods for Integral Equations (1985), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0592.65093
[3] Maleknejad, K.; Mirzaee, F., The preconditioned conjugate gradient method for solving convolution-type integral equations, Int. J. Eng. Sci, 14, 1-11 (2003)
[4] Maleknejad, K.; Hadizadeh, M., A new computational method for Volterra-Fredholm integral equations, Comput. Math. Appl, 37, 9, 1-8 (1999) · Zbl 0940.65151
[5] Maleknejad, K.; Rostami, D., Preconditioners for solving stochastic boundary integral equations with weakly singular kernels, Computing, 63, 47-67 (1999) · Zbl 0949.65143
[6] Perlmutter, M.; Siegel, R., Effect of specularly reflecting grey surface on thermal radiation through a tube and from its heated wall, ASME J. Heat Transfer, 85, 55-62 (1963)
[7] Ren, Y.; Zhang, B.; Qiao, H., A simple Taylor-series expansion method for a class of second kind integral equations, J. Comput. Appl. Math, 110, 15-24 (1999) · Zbl 0936.65146
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.