HIGHLY ACCURATE DISCRETE METHODS FOR NONLINEAR PROBLEMS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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We study in this work the acceleration of the convergence of discretization algorithms for the solution of nonlinear operator equations in Banach spaces. Two methods, usually used with finite difference schemes, are extended to this general case and their asymptotic properties are established. These are the Successive Extrapolations method Richardsons extrapolation to the limit, Romberg integration, and the Iterated Deferred Corrections method Foxs difference correction. The application of these procedures to nonlinear boundary value problems in one and two dimensions is discussed in detail and a complete set of numerical examples is presented. This includes the problem of finding periodic solutions in the case of forced oscillations. Author
- Theoretical Mathematics