On a fourth-order unconditionally stable scheme for damped second-order systems |
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Authors: | Steven M Serbin |
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Affiliation: | Department of Mathematics, University of Tennessee, Knoxville, TN 37916, U.S.A. |
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Abstract: | We consider the damped second-order system (M, C, K symmetric, positive definite n × n matrices) by conversion to an equivalent first-order system We demonstrate that an algorithm proposed by Fairweather for the implementation of the (2, 2) Padé approximation of the exponential matrix for approximating the solution of homogeneous first-order systems extends advantageously to this case, yielding an unconditionally stable fourth-order scheme with the feature that the approximating equations decouple. As a result we are required only to solve one symmetric complex n × n system of linear algebraic equations at each time step, with a fixed matrix which may be decomposed into triangular factors at the outset. We also consider iterative schemes involving only real, positive definite, symmetric n × n matrices. Numerical results are included. |
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