Least square approximation of a nonlinear ordinary differential equation
The subject of the paper is an optimal linearization method for nonlinear ordinary differential equations. Results concerning an earlier proposed approximation are presented. The main results stipulate that the proposed approximation is of order two with respect to the initial value, and is generally of the same order as the nonlinearity. Necessary and sufficient conditions are given for uniqueness of the elements of the sequence determined in the course of the optimal approximation. Several examples are included showing satisfactory adequacy of approximate results compared to the exact ones.
nonlinear ordinary differential equations
scientific article; zbMATH DE number 915114
scientific article