Fluctuationlessness Theorem and its Application to Boundary Value Problems of ODEs

摘要

A numerical method based on Fluctuationlessness Approximation, which was developed recently, is constructed for solving Boundary Value Problems of Ordinary Differential Equations on appropriately defined Hilbert Spaces. The numerical solution is written in the form of a Maclaurin series. The unknown coefficients of this series are determined by constructing an (n - 2) unknown containing linear system of equations. The eigenvalues of the independent variable's matrix representation are used in the construction of the matrices and the vectors of the linear system. The numerical solution obtained by Fluctuationlessness Approximation is then compared with the Maclaurin coefficients of the analytical solution to observe the quality of the convergence. Some illustrative examples are presented in order to give an idea about the efficiency of the method explained here.