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The Compound Matrix Method for Multi‐Point Boundary‐Value Problems
Author(s) -
Ivansson S.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970771009
Subject(s) - ode , ordinary differential equation , boundary value problem , matrix (chemical analysis) , mathematics , homogeneous , mathematical analysis , computation , point (geometry) , differential equation , algorithm , geometry , materials science , combinatorics , composite material
The compound matrix method is generalized to handle multi‐point boundary‐value problems for first‐order ordinary differential‐equation (ODE) systems. A general treatment is given, covering all dimensions of the linear ODE system and different locations of the linear boundary conditions in a unified way. The back‐propagation step is performed in a new and simplified way. It is shown how local particular solutions can be used for reduction to a homogeneous ODE system. As an application case, efficient techniques are developed for wave‐propagation computations for range‐independent multi‐region fluid‐solid media. Thick homogeneous layers can be handled reliably without layer splitting.