Geodesic
An analysis of multistep methods for solving integral-algebraic equations: Construction of stability domains
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 9, pp. 1448-1459 
M. V. Bulatov; O. S. Budnikova. An analysis of multistep methods for solving integral-algebraic equations: Construction of stability domains. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 9, pp. 1448-1459. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_9_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Systems of Volterra integral equations with identically singular matrices in the principal part (called integral-algebraic equations) are examined. Multistep methods for the numerical solution of a selected class of such systems are proposed and examined.

[1] Brunner H., Collocation method for Volterra integral and related functional equations, University Press, Cambridge, 2004 | MR | Zbl

[2] Ten Men Yan, Priblizhennoe reshenie lineinykh integralnykh uravnenii Volterra I roda, Dis. ... kand. fiz. matem. nauk, Irkutsk, 1985

[3] Brunner H., van der Houwen P. J., The numerical solution of Volterra equations, CWI Monographs, 3, North-Holland, Amsterdam, 1986 | MR | Zbl

[4] Linz P., “A survey of methods for the solution of Volterra integral equations of the first kind”: H. Brunner, Collocation Metthods for Volterra Integral and Related Functions, University Press, Cambridge, 2004

[5] Bulatov M. B., Budnikova O. S., “Chislennoe reshenie integro-algebraicheskikh uravnenii mnogoshagovymi metodami”, Zh. vychisl. matem. i matem. fiz., 52:5 (2012), 829–839 | Zbl

[6] Kauthen J.-P., “The numerical solution of integral-algebraic equations of index-1 by pollinomial spline collocation methods”, Math. Comp., 236 (2000), 1503–1514 | DOI | MR

[7] Hadizadeh M., Ghoreishi F., Pishbin S., “Jacobi spectral solution for integral algebraic equations of index-2”, Appl. Numer. Math., 61:1 (2011), 131–148 | DOI | MR | Zbl

[8] Pishbin S., Ghoreisjii F., Hadizadeh M., “The semi'explicit Volterra integral algebraic equations with weakly singular kernel: The numerical treatments”, J. Comput. and Appl. Math., 245:1 (2013), 121–132 | DOI | MR | Zbl

[9] Bulatov M. V., Budnikova O. S., Pishbin S., “Issledovanie ustoichivosti mnogoshagovykh metodov dlya integro-algebraicheskikh uravnenii”, Analiticheskaya mekhanika, ustoichivost i upravlenie, Tr. Kh Mezhdunar. Chetaevskoi konferentsii (Kazan, 2012), v. 1, 72–80

[10] Chistyakov V. F., “O singulyarnykh sistemakh obyknovennykh differentsialnykh uravnenii i ikh integralnykh analogakh”, Funktsii Lyapunova i ikh primeneniya, Nauka, Novosibirsk, 1987, 231–239

[11] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR

[12] Kershaw D., Volterra equations of the second kind, Delves Walsh, 1974, 140–161 | MR

[13] Kholl Dzh., Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979