On the numerical solution of implicit two-point boundary-value problems

This paper presents an application of the so-called modified quasilinean'zation method to the solution nonlinear, implicite two-point boundary-value problems. Analogously as in the explicit case the resulting algorithm exhibits the descent property in the auxiliary performance index which measures the cumulative error in the differential equations and the boundary conditions. Practical importance of this algorithm is illustrated on several examples solved in detail. A com­ parison with the classical Newton-Raphson method is also included.