Abstract
In the preceding chapter, we discussed various applications of the theory of dynamic programming to the analytic and computational treatment of the two-dimensional potential equation. A drawback, which becomes major in three dimensions, is the high dimension of the associated Riccati equations. In this chapter we show how this problem can be overcome at the expense of increasing the number of one dimensional operations that are performed. The same method can be applied to many other types of partial differential equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography and Comments
E. Angel and R. Bellman, ’Reduction of Dimensionality for the Potential Equation using Dynamic Programming’, Unititas Mathematica 1 (1972) 181–190
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 D. Reidel Publishing Company
About this chapter
Cite this chapter
Bellman, R., Adomian, G. (1985). The Three Dimensional Potential Equation. In: Partial Differential Equations. Mathematics and Its Applications, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5209-6_9
Download citation
DOI: https://doi.org/10.1007/978-94-009-5209-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8804-6
Online ISBN: 978-94-009-5209-6
eBook Packages: Springer Book Archive