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Nonlinear Theory and Its Applications, IEICE
Vol. 4 (2013) No. 1 pp. 23-33



Special section on Recent Progress in Verified Numerical Computations

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.

Copyright © 2013 The Institute of Electronics, Information and Communication Engineers

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