Angel E., Bellman R. Dynamic Programming and Partial Differential Equations
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Mathematics in Science and Engineering, Volume 88.Academic Press, 1972. 204 pages.A major task of contemporary mathematical analysis is that of providing computer algorithms for the numerical solution of partial differential equations of all types. This task requires a motley mixture of methods. In this book we wish to show first that dynamic programming and invariant imbedding furnish some powerful techniques for the solution of linear elliptic and parabolic partial differential equations over regular and irregular regions. Nonlinear equations are made accessible by the use of quasilinearization which can be combined with the earlier procedures to study identification and inverse problems. What is quite important is that these algorithms are straightforward, easily learned, readily programmed, and easily used.
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