# A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.

Original language English 239-251 13 Applied Mathematics and Computation 276 https://doi.org/10.1016/j.amc.2015.12.021 Published - 2016 Mar 5 Yes

### Fingerprint

Numerical Verification
Functional equation
Nonlinear Equations
Computer-assisted Proof
Iteration
Nonlinear Partial Differential Equations
Partial differential equations
Differential equations
Differential equation
Form

### Keywords

• Differential equation
• Functional equation
• Newton-like iteration
• Residual form

### ASJC Scopus subject areas

• Computational Mathematics
• Applied Mathematics

### Cite this

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. / Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

In: Applied Mathematics and Computation, Vol. 276, 05.03.2016, p. 239-251.

Research output: Contribution to journalArticle

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