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Published 1985 | Published
Journal Article Open

Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems


We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations.

Additional Information

© 1985 Society for Industrial and Applied Mathematics. Received by the editors November 22, 1982, and in revised form June 12, 1984. The research of this author was supported in part by the U.S. Department of Energy under contract EY-76-S-03-0767, Project Agreement 12, and by the Army Research Office under contract DAAG 29-78-C-0011. The authors would like to thank Professor R. B. Simpson and the referees for most helpful comments and suggestions.

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