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

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.