Properties of a Semi-discrete Approximation to the Beam Equation

The solution of the equation w(x)u_tt+[p(x)u_xx]_xx = 0, 0 < x < L, t > 0, where it is assumed that w and p are positive on the interval[O, L], is approximated by using the method of straight lines.The resulting approximation is a linear system of differentialequations with coefficient matrix S. The matrix S is studiedunder very general boundary conditions which result in a conservativesystem. In all cases the matrix S is either an oscillation matrixor possesses nearly all the properties of an oscillation matrix.