Geodesic
The method of normal splines for linear implicit differential equations of second order
Lobachevskii journal of mathematics, Tome 20 (2005), pp. 59-75

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The method of normal splines is specified for the initial and boundary-value problems for systems of linear ordinary differential equations of second order, possible being stiff or unresolved with respect to derivatives (differential-algebraic equations), without their reduction to first order ones. The algorithm of nonuniform collocation grid creation for stiff problems is described. Results of numerical solution to test problems, including linear mathematical physics boundary-value problem of the second order are given. Numerical schemes for the last case are based on the method of lines.
Keywords: normal splines, singular differential-algebraic equations, adaptive grids, partial differential equations, method of lines. 
@article{LJM_2005_20_a4,
     author = {V. K. Gorbunov and A. Gorobetz and V. Sviridov},
     title = {The method of normal splines for linear implicit differential equations of second order},
     journal = {Lobachevskii journal of mathematics},
     pages = {59--75},
     publisher = {mathdoc},
     volume = {20},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2005_20_a4/}
}
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V. K. Gorbunov; A. Gorobetz; V. Sviridov. The method of normal splines for linear implicit differential equations of second order. Lobachevskii journal of mathematics, Tome 20 (2005), pp. 59-75. http://geodesic.mathdoc.fr/item/LJM_2005_20_a4/