Viktor Verbitskyi, Anton Loktev


A scheme of the finite element method for solving a boundary value problem for an ordinary differential equation with piecewise constant coefficients is proposed.

The basic functions of finite-dimensional subspaces are constructed using solutions of the Dirichlet problem for a homogeneous differential equation on a finite element.

Those solutions are easy to construct if all the points of discontinuity of the equation coefficients  are contained among the grid nodes.

The finite element solution of the boundary value problem coincides with the exact solution at the nodes of the grid.

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