Derivation and validation of an initial-value method for certain nonlinear two-point boundary-value problems

DOI10.1007/BF00925743zbMath0177.35104OpenAlexW2087750161MaRDI QIDQ2533788

Robert E. Kalaba, Harriet H. Kagiwada

Publication date: 1968

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00925743

zbMATH Keywords

ordinary differential equations

Related Items (17)

The work of Richard Bellman—I. optimization ⋮ A Cauchy system for the Green's function and the solution of a two-point boundary value problem ⋮ A rapprochement of the theories of radiative transfer and linear stochastic estimation ⋮ Suboptimal control of systems with multiple delays ⋮ Optimal trajectories for quadratic variational processes via invariant imbedding ⋮ Method of particular solutions for linear, two-point boundary-value problems ⋮ Exact solution of Pontryagin's equations of optimal control. I ⋮ A one-sweep numerical method for vector-matrix difference equations with two-point boundary conditions ⋮ Invariant imbedding and the numerical determination of Green's functions ⋮ An initial-value method for the solution of certain nonlinear diffusion equations in biology ⋮ Proof of the basic invariant imbedding method for Fredholm integral equations with deplacement kernels. I, II ⋮ Dynamic programming and optimal trajectories for quadratic variational processes ⋮ Some invariance principles for two-point boundary value problems ⋮ On the imbedding solution of a class of optmal control problems ⋮ Initial value methods in detection and communication theory ⋮ Invariant imbedding and the simplest problem in the calculus of variations ⋮ Interval length imbedding for nonlinear two-point boundary-value problems

Cites Work

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• A practical method for determining Green's functions using Hadamard's variational formula
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• Challenges of modern control theory
• INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS
• ON THE FUNDAMENTAL EQUATIONS OF INVARIANT IMBEDDING, I
• Invariant imbedding and the numerical integration of boundary-value problems for unstable linear systems of ordinary differential equations

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