QUASI-LINEARIZATION AND APPROXIMATE QUASI-LINEARIZATION FOR LIDSTONE BOUNDARY-VALUE-PROBLEMS

Quasilinearization technique has been applied to a general nonlinear Lidstone boundary value problem for the construction of a sequence of its approximate solutions (x„(f)). Sufficient conditions for the linear as well as quadratic convergence of (x„(f)) to the unique solution x*(f) of the boundary value problem have been provided. In practice one always computes (y„(r)), an approximation to (x„(f)). Necessary and sufficient conditions for the convergence of (yw(f)) to x*(f) have also been established. © 1992, Taylor & Francis Group, LLC. All rights reserved.