论文信息 - An Investigation Into Direct Numerical Methods for Solving Some Calculus of Variations Problems. Part 1 - Second Order Methods

An Investigation Into Direct Numerical Methods for Solving Some Calculus of Variations Problems. Part 1 - Second Order Methods

/ is a given function of three variables. Boundary conditions on y(x) at x = a or b may or may not be given. In general, however, in this paper we have considered them to be given. Problems arise in this form in both scientific and industrial fields. Most analytic and numerical methods of solving this problem to date have used the fact that the problem is equivalent to solving a boundary value, second order differential equation. This equation, known as Euler's equation, is derived in many well known texts (for example Elsgolc, 1961) and is given byt

B. T. Allen

[1] J. H. Wilkinson. Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection , 1962 .

[2] A. Rachman. Computation of rotational energy levels of rigid asymmetric top molecules , 1965, Comput. J..

[3] J. G. F. Francis,et al. The QR Transformation A Unitary Analogue to the LR Transformation - Part 1 , 1961, Comput. J..

[4] A. J. Fox,et al. On Finding the Eigenvalues of Real Symmetric Tridiagonal Matrices , 1966, Comput. J..

[5] Eric L. Jones,et al. Note on an Alternate Method for the Computation of Rotational Energy Levels of Rigid Asymmetric Top Molecules , 1966, Comput. J..

[6] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .