Advanced Engineering Mathematics: Maple Computer Guide
Advanced Engineering Mathematics: Maple Computer Guide
Fluctuationlessness theorem and its application to boundary value problems of ODEs
WSEAS Transactions on Mathematics
Fluctuationlessness theorem and its application to boundary value problems of ODEs
MAASE'09 Proceedings of the 2nd WSEAS international conference on Multivariate analysis and its application in science and engineering
AICT'11 Proceedings of the 2nd international conference on Applied informatics and computing theory
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This paper presents a new method based on Fluctuationlessness Theorem that was proven recently for getting the numerical solutions to the Ordinary Differential Equations over appropriately defined Hilbert Spaces. Approximations to the solution are evaluated at a series of discrete points. These points are constructed as the eigenvalues of the independent variable's matrix representation restricted to an n dimensional subspace of the Hilbert Space under consideration. The approximated solution is written in the form of an n-th degree polynomial of the independent variable. The unknown coefficients are found by setting up a system of linear equations such that this solution satisfies the initial condition and the differential equation at the grid points. The numerical quality of the solution can be increased by taking greater values of n.