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2014 | 12 | 2 | 308-321
Tytuł artykułu

Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral equations of the first kind in which the determinant of the kernel matrix k(t, x) vanishes when t = x. Finally, the third part of the work is devoted to the analysis of degenerate integro-differential systems. The aim of the paper is to specify conditions which are sufficient for the existence of a unique continuous solution to the above problems. Theoretical findings are illustrated by a number of examples.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
2
Strony
308-321
Opis fizyczny
Daty
wydano
2014-02-01
online
2013-11-21
Twórcy
autor
Bibliografia
  • [1] Boyarintsev Yu., Methods of Solving Singular Systems of Ordinary Differential Equations, Pure Appl. Math. (N.Y.), John Wiley & Sons, Chichester, 1992
  • [2] Brenan K.E., Campbell S.L., Petzold L.R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Classics Appl. Math., 14, SIAM, Philadelphia, 1996
  • [3] Brunner H., Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge Monogr. Appl. Comput. Math., 15, Cambridge University Press, Cambridge, 2004 http://dx.doi.org/10.1017/CBO9780511543234
  • [4] Brunner H., Bulatov M.V., On singular systems of integral equations with weakly singular kernels, In: Optimization Methods and their Applications, Irkutsk, July 5–12, 1998, Melentiev Energy Systems Institute, Irkutsk, 1998, 64–67
  • [5] Brunner H., van der Houwen P.J., The Numerical Solution of Volterra Equations, CWI Monogr., 3, North-Holland, Amsterdam, 1986
  • [6] Bulatov M.V., Transformation of algebro-differential systems of equations, Comput. Math. Math. Phys., 1994, 34(3), 301–311
  • [7] Bulatov M.V., Integro-differential systems with a degenerate matrix multiplying the derivative, Differ. Equ., 2002, 38(5), 731–737 http://dx.doi.org/10.1023/A:1020227128158
  • [8] Bulatov M.V., Chistyakova E.V., On a family of singular integro-differential equations, Comput. Math. Math. Phys., 2011, 51(9), 1558–1566 http://dx.doi.org/10.1134/S0965542511090065
  • [9] Bulatov M.V., Lee M.-G., Application of matrix polynomials to the analysis of linear differential-algebraic equations of higher order, Differ. Equ., 2008, 44(10), 1353–1360 http://dx.doi.org/10.1134/S0012266108100017
  • [10] Bulatov M.V., Lima P.M., Two-dimensional integral-algebraic systems: Analysis and computational methods, J. Comput. Appl. Math., 2011, 236(2), 132–140 http://dx.doi.org/10.1016/j.cam.2011.06.001
  • [11] Chistyakov V.F., Algebro-Differential Operators with a Finite-Dimensional Kernel, Nauka, Novosibirsk, 1996 (in Russian)
  • [12] Chistyakov V.F., On singular systems of ordinary differential equations and their integral analogs, In: Lyapunov Functions and their Applications, Nauka, Novosibirsk, 1987, 231–239 (in Russian)
  • [13] Gantmacher F.R., The Theory of Matrices, 1&2, Chelsea Publishing, New York, 1977
  • [14] Griepentrog E., März R., Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Texte Math., 88, Teubner, Leipzig, 1986
  • [15] Hadizadeh M., Ghoreishi F., Pishbin S., Jacobi spectral solution for integral-algebraic equations of index-2, Appl. Numer. Math., 2011, 61(1), 131–148 http://dx.doi.org/10.1016/j.apnum.2010.08.009
  • [16] Hairer E., Wanner G., Solving Ordinary Differential Equations, II, Springer Ser. Comput. Math., 14, Springer, Berlin, 1991 http://dx.doi.org/10.1007/978-3-662-09947-6
  • [17] Kunkel P., Mehrmann V., Differential-Algebraic Equations, EMS Textbk. Math., European Mathematical Society, Zürich, 2006
  • [18] Lamour R., März R., Tischendorf C., Differential-Algebraic Equations: A Projector Based Analysis, Differ.-Algebr. Equ. Forum, Springer, Heidelberg, 2013
  • [19] Lancaster P., Theory of Matrices, Academic Press, New York, London, 1969
  • [20] Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives, Gordon and Breach, Yverdon, 1993
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0334-5
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