Properties of a Semi-discrete Approximation to the Beam Equation |
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Authors: | SWEET ROLAND A |
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Institution: |
Department of Computer Science, Cornell University Ithaca, New York, U.S.A.
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Abstract: | The solution of the equation w(x)utt+p(x)uxx]xx = 0, 0 < x < L, t > 0, where it is assumed that w and p are positive on the intervalO, 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. |
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