Abstract
Recently, several methods to the computer-assisted existence proof of solutions for various differential equations have been developed. However, there are very few approaches for partial differential equations. As far as we know, there are only two methods, that is, Nakao’s method (e.g. Nakao 1993) using C 0 finite element and explicit error estimates, and Plum’s method (e.g. Plum 1994) using C 1-class approximate solution with high accuracy and an exact eigenvalue enclosure for a linearized operator. Almost all papers by these authors deal with elliptic equations.
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Minamoto, T. (2001). Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6280-4_17
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DOI: https://doi.org/10.1007/978-3-7091-6280-4_17
Publisher Name: Springer, Vienna
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