Abstract
An efficient procedure of Lie-algebraic discrete approximation for nonlinear evolution equations in a Banach space is developed. A convergent approximation is constructed, and the analysis of stability is carried out. For the Lie-algebraic discrete approximation of linear and nonlinear differential operators, an application of the multivariate form of Lagrangian interpolating schemes in star-shaped domains is suggested.
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Luśtyk, M. Lie-Algebraic Discrete Approximation for Nonlinear Evolution Equations. Journal of Mathematical Sciences 109, 1169–1172 (2002). https://doi.org/10.1023/A:1013780223937
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DOI: https://doi.org/10.1023/A:1013780223937