Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:C3L-A

Session:

Number:441

A verified continuation algorithm for solution curve of nonlinear elliptic equations

Akitoshi Takayasu,  Shin'ichi Oishi,  

pp.441-444

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.441

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Summary:
In this article, a verified numerical continuation method is proposed for a nonlinear operator equation. Numerical continuation method calculates solution curve of parameterized nonlinear equation approximately. Although the verified numerical computation yields point wise proofs of the solution curve, continuous branch following is difficult to be proved. On the basis of the implicit function theorem, a smooth solution branch of Ambrosetti-Prodi's type problem is obtained by our verified continuation approach.

References:

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