TY - BOOK ID - 1185466 TI - Invariant imbedding; : proceedings of the Summer Workshop on Invariant Imbedding, held at the University of Southern California, June - August 1970 AU - Bellman, Richard AU - Denman, Eugene D. AU - Summer Workshop on Invariant Imbedding (1970 : University of Southern California) PY - 1971 VL - 52 SN - 3540055495 0387055495 364246274X 9780387055497 PB - Berlin: Springer, DB - UniCat KW - Numerical solutions of differential equations KW - Business & Economics KW - Economic Theory KW - 681.3*G17 KW - 681.3*G19 KW - Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) KW - Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) KW - 681.3*G19 Integral equations: Fredholm equations; integro-differential equations; Volterra equations (Numerical analysis) KW - 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) KW - Invariant imbedding KW - Differential equations KW - Integral equations KW - Equations différentielles KW - Equations intégrales KW - Plongement invariant KW - Équations aux dérivées partielles KW - Programmation (mathématiques) KW - Équations aux dérivées partielles KW - Programmation (mathématiques) KW - Equations differentielles UR - https://www.unicat.be/uniCat?func=search&query=sysid:1185466 AB - Imbedding is a powerful and versatile tool for problem­ solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa­ tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro­ cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy. ER -