Abstract
In this chapter we introduce the basic ideas of the method of invariant imbedding, relating to the simple case of particle transport in a one-dimensional medium. The nonlinear equations for the emergent fluxes are deduced by particle counting techniques as well as by analytical procedures. The importance of conservation laws, positivity of the fluxes, are discussed. A method of linearizing the equations by a method dictated by the physics of the problem is elaborated. In the succeeding chapters, these methods are adapted to the case of wave propagation.
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References
Bellman, R., R. Kalaba, and G.M. Wing, ‘Invariant Imbedding and Mathematical Physics — I: Particle Processes’, Journal of Mathematical Physics 1 (1960), 280–308.
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© 1986 D. Reidel Publishing Company
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Bellman, R., Vasudevan, R. (1986). Invariant Imbedding. In: Wave Propagation. Mathematics and Its Applications, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5227-0_3
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DOI: https://doi.org/10.1007/978-94-009-5227-0_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8811-4
Online ISBN: 978-94-009-5227-0
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