Quasilinearization and approximate quasilinearization for lidstone boundary value problems

Abstract

Quasilinearization technique has been applied to a general nonlinear Lidstone boundary value problem for the construction of a sequence of its approximate solutions {x_n (t)}. Sufficient conditions for the linear as well as quadratic convergence of {x_n (t)} to the unique solution x ^∗(t) of the boundary value problem have been provided. In practice one always computes {y_n (t)}an approximation to {x_n (t)}. Necessary and sufficient conditions for the convergence of {y_n (t)} to x ^∗(t) have also been established.

Keywords:

• Quasilinearization
• Approximate Quasilinearization
• Lidstone Boundary Value Problems

C.R. Categories:

• G.1.7