Quasilinearization and approximate quasilinearization 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 {xn (t)}. Sufficient conditions for the linear as well as quadratic convergence of {xn (t)} to the unique solution x ∗(t) of the boundary value problem have been provided. In practice one always computes {yn (t)}an approximation to {xn (t)}. Necessary and sufficient conditions for the convergence of {yn (t)} to x ∗(t) have also been established.

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