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A nonlinear adaptive multiresolution method in finite differences with incremental unknowns. (English) Zbl 0836.65114
A new method for the calculation of unstable solutions of nonlinear eigenfunction problems is proposed. The method is derived from the classical Marder-Weitzner scheme (MW) which is treated as a nonlinear Richardson method. The method is generalized with the utilization of the incremental unknowns inducing the minimizing relaxation parameter in the embedded hierarchical subspaces. In this way the author obtains generalisations of the MW and linear Richardson algorithms. The numerical illustrations allowing comparisons between different versions of the MW method (for nonlinear eigenfunction problems) point out a better rate of convergence of the new algorithms.
Reviewer: P.Burda (Praha)

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
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