Abstract
The purpose of this chapter is to present a new method for treating a class of partial differential equations. The method depends upon the fact that the calculus of variations can be considered to be a continuous multistage decision process. Hence, we use the theory of dynamic programming to obtain a crucial relation.
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Bibliography and Comments
R. Bellman, ‘A New Method for Treating a Class of Nonlinear Partial Differential Equations’, Nonlinear Analysis, Theory, Methods, and Applications, Vol. 3, No. 5, pp. 721–722.
R. Bellman, Methods of Nonlinear Analysis, Vol. II, Academic Press, Inc., New York, 1973.
E.S. Lee, Quasilinearization and Invariant Imbedding, Academic Press, Inc., New York, 1968.
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© 1985 D. Reidel Publishing Company
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Bellman, R., Adomian, G. (1985). Quasilinearization and a New Method of Successive Approximations. In: Partial Differential Equations. Mathematics and Its Applications, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5209-6_5
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DOI: https://doi.org/10.1007/978-94-009-5209-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8804-6
Online ISBN: 978-94-009-5209-6
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