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A smooth solution to a linear system of singular ODEs. (English) Zbl 1275.34014

Summary: For a linear system of singular ordinary differential equations, necessary and sufficient conditions are established for the existence of a unique \(C^m\)-smooth solution. A reduction to cordial Volterra integral equations is used.

MSC:

34A30 Linear ordinary differential equations and systems
45D05 Volterra integral equations
Full Text: DOI

References:

[1] Auzinger, W., Koch, O. and Weinmüller, E., Analysis of a new error estimate for collocation methods applied to singular boundary value problems. SIAM J. Numer. Anal. 42 (2005), 2366 - 2386. · Zbl 1087.65082 · doi:10.1137/S0036142902418928
[2] Baouendi M. S. and Goulaouic, C., Singular nonlinear Cauchy problems. J. Diff. Equ. 22 (1976), 268 - 291. · Zbl 0344.35012 · doi:10.1016/0022-0396(76)90028-0
[3] Brunner, H., Collocation Methods for Volterra Integral and Related Functional Equations. Cambridge: Cambridge Univ. Press 2004. · Zbl 1059.65122 · doi:10.1017/CBO9780511543234
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