Richard Bellman – Communications of the ACM

Research and Advances Oct 1 1966

Mathematical experimentation in time-lag modulation

Equations of the form du/dt = g(u(t), u(h(t))) arise in a number of scientific contexts. The authors point out some interesting properties of the solution of u′(t) = -u(t - 1 - k sin &ohgr;t) + sin at. These properties were obtained by means of numerical solution.

Author Archives

Research and Advances Jul 1 1966

Quasilinearization and the calculation of eigenvalues

Research and Advances Aug 1 1965

Nonlinear extrapolation and two-point boundary value problems

It is suggested that the convergence properties of the usual Picard successive approximation scheme may be improved through use of nonlinear extrapolation techniques. A numerical example is provided.

Research and Advances Jun 1 1961

On the approximation of curves by line segments using dynamic programming

Artificial Intelligence and Machine Learning

Research and Advances May 1 1961

Successive approximations and computer storage problems in ordinary differential equations

Computing Applications

Research and Advances Apr 1 1961

Some numerical experiments using Newton’s method for nonlinear parabolic and elliptic boundary-value problems

Using a generalization of Newton's method, a non-linear parabolic equation of the form ut - uxx = g(u), and a non-linear elliptic equation uxx + uyy = eu, are solved numerically. Comparison of these results with results obtained using the Picard iteration procedure show that in many cases the quasilinearization method offers substantial advantages in both time and accuracy.

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