A NUMERICAL-METHOD OF SOLVING INVERSE PROBLEMS FOR NONLINEAR DIFFERENTIAL-EQUATIONS

A numerical method is proposed for solving the inverse problem for a system of non-linear ordinary differential equations with an unknown finite-dimensional parameter vector. It is proved that the method has quadratic rate of convergence, equal to that of the Newton-Raphson method for solving algebraic equations, and Bellman's quasilinearization method for solving differential equations. Examples are given in which a Lotka-Volterra system and Lorenz random model are identified. Results are obtained on an IBM AT computer.