On the choice of an appropriate imbedding algorithm for the solution of unstable linear boundary value problems

作者: F. Breitenecker

DOI: 10.1007/BF02259912

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摘要: The method of Extended (or Generalized) Invariant Imbedding solves unstable linear boundary value problems in a stable manner. requires the integration one four different matrix Riccati differential equations (four algorithms). In this contribution questions existence, stability, boundedness and error propagation these are discussed order to help user choose appropriate algorithm.

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G. H. Meyer, On a General Theory of Characteristics and the Method of Invariant Imbedding SIAM Journal on Applied Mathematics. ,vol. 16, pp. 488- 509 ,(1968) , 10.1137/0116039
F. Breitenecker, Invariant imbedding and multiple shooting for the solution of unstable linear boundary value problems Applied Mathematics and Computation. ,vol. 9, pp. 235- 244 ,(1981) , 10.1016/0096-3003(81)90014-X
J.S. Bramley, The numerical solution of unstable ordinary differential equations Applied Mathematics and Computation. ,vol. 4, pp. 307- 316 ,(1978) , 10.1016/0096-3003(78)90002-4