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- W1986291209 abstract "We give a theoretical result with respect to numerical verification of existence and local uniqueness of solutions to fixed-point equations which are supposed to have Frechet differentiable operators. The theorem is based on Banach's fixed-point theorem and gives sufficient conditions in order that a given set of functions includes a unique solution to the fixed-point equation. The conditions are formulated to apply readily to numerical verification methods. We already derived such a theorem in [11], which is suitable to Nakao's methods on numerical verification for PDEs. The present theorem has a more general form and one may apply it to many kinds of differential equations and integral equations which can be transformed into fixed-point equations." @default.
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- W1986291209 date "2011-11-01" @default.
- W1986291209 modified "2023-09-23" @default.
- W1986291209 title "A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations" @default.
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- W1986291209 doi "https://doi.org/10.1080/01630563.2011.594348" @default.
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