A simple numerical verification method for differential equations based on infinite dimensional sequential iteration

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概要

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• This paper describes a numerical verification of solutions for infinite dimensional functional equations based on residual form and sequential iteration. Comparing with other verification procedures as typified by Newton-type iterations, the proposed algorithm can be done at low computational cost, although it needs that the formulated compact map is retractive in some neighborhood of the fixed-point to be verified. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations will be shown.

著者

• WATANABE Yoshitaka

  Research Institute for Information Technology, Kyushu University

• Watanabe Yoshitaka

  Research Institute For Information Technology Kyushu University

関連論文

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• A simple numerical verification method for differential equations based on infinite dimensional sequential iteration
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