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This paper presents a numerical computer method of nonlinear two-point boundary value problems using a formal linearization method. We have considered a nonlinear system with two-point boundary conditions. The nonlinear system is transformed into a linear system by the formal linearization method. The transforming function is given as a solution of a partial differential equation and is solved by Taylor or orthogonal expansions. The missing values at the boundary points are evaluated using the Newton method. As a result, the nonlinear twopoint boundary value problem becomes a nonlinear initial value problem which can be easily solved. The error bounds of the presented method are also investigated. Two examples are included to demonstrate the effectiveness of this method. One of them is the case of a transforming function of polynomials, the other being the case of a nonlinear optimal control problem using the maximum principle.

A Computer Method and Error Bounds of Nonlinear Two-Point Boundary Value Problems Using Formal Linearization