## V. Gorbunov, A. Gorobetz, and V. Sviridov

# The method of normal splines for linear implicit differential equations of second order

## (*Lobachevskii Journal of Mathematics, Vol.20, pp.59-75*)

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.

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