Abstract: A proposed method for finding an approximate solution of the nonlinear ordinary differential equations two-point boundary value problem is proposed. It simplifies the problem approximately to a problem of solving a set of nonlinear algebraic equations. The basic idea of the method is to utilize the properties of orthogonal polynomials and the approximate operational matrices of the nonlinear functional f(x(t),u(t),t), and also the transformation matrix between the back vector and the current time vector for the general orthogonal polynomials. A method for solving the nonlinear two-point boundary value problems for descriptor systems is also given.

Key words: nonlinear systems, two-point boundary value problems, approximate solution, orthogonal polynomials

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