×

The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials. (English) Zbl 1023.65147

Summary: A Taylor method is developed to find the approximate solution of high-order linear Volterra-Fredholm integro-differential equations under the mixed conditions in terms of Taylor polynomials about any point. In addition, examples that illustrate the pertinent features of the method are presented, and the results of study are discussed.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] El-gendi, S. E., Chebyshev solution of differential, integral and integro-differential equations, Comp. J., 12, 282-287 (1969) · Zbl 0198.50201
[2] Kaçar, A.; Mamedov, Y. D., nce çubu \(ğ\) u ensneklik probleminin iki yaklaş1k metodla çözümü, Azerb. Ilm. Akad.-nin Haber. Sibernetika, 21-24, 109, 1-11 (1996)
[3] Kanwal, R. P.; Liu, K. C., A Taylor expansion approach for solving integral equations, Int. J. Math. Educ. Sci. Technol, 20, 3, 411-414 (1989) · Zbl 0683.45001
[4] Kauthen, J. P., Continuos time collocation methods for Volterra-Fredholm integral equations, Numer. Math., 56, 409-424 (1989) · Zbl 0662.65116
[5] M.A. Krasnosel’skij, A.V. Sobolev, Positive Linear Systems, Helderman, Berlin, 1989; M.A. Krasnosel’skij, A.V. Sobolev, Positive Linear Systems, Helderman, Berlin, 1989 · Zbl 0674.47036
[6] P.E. Lewis, J.P. Word, The Finite Element Method, Addison-Wesley, Reading, MA, 1991; P.E. Lewis, J.P. Word, The Finite Element Method, Addison-Wesley, Reading, MA, 1991
[7] Sezer, M., Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol., 25, 5, 625-633 (1994) · Zbl 0823.45005
[8] Sezer, M., A method for the approximate solution of the second-order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol., 27, 6, 821-834 (1996) · Zbl 0887.65084
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.