 About 28,900 results  books.google.com Allen, B. T. (1966) "An investigation into direct numerical methods for solving
some calculus of variations problems. ... Baxley, J. W. (1972a) "Eigenvalues of
singular differential operators by finite difference methods", J.M.A.A. 38. 244– 254
. 

 books.google.com 280; see also under the individual equation names differential operator, see
linear differential operator differentiation and ... estimation of eigenvalues for a
linear differential operator, 3514; for a matrix, 3569, 402 Euler method,
numerical, ... 

 books.google.com D At the present time there are no general quantitative results controlling the rate
of variation of the eigenvalues under small ... Many numerical methods of
computing the eigenvalues of such operators are based upon applying the
variational ... 

 books.google.com Numerical and Quantitative Analysis. Pitman: ... The Convergence of a New
Method for Calculating Lower Bounds to Eigenvalues. ... Eigenvalue inclusions
for secondorder ordinary differential operators by a numerical homotopy method. 

 books.google.com A symmetric matrix with all positive eigenvalues is said to be positive definite.
Note also that the eigenvectors v(k) defined in (13.14) are related to the
eigenfunctions v(k)(x) = sin(kπx), k = 1,2,... of the differential operator − d2 dx2 . 

 books.google.com Through a simple and systematic algorithm, which treats the differential operator
and supplementary conditions with ... The tau method is well adapted to produce
accurate approximations in the numerical treatment of differential eigenvalue ... 

 books.google.com D One popular method to approximate many eigenvalues is the spectral method.
... INFINITE INTERVALS Up to now we have assumed “sufficient regularity” of the
differential operator when developing theory for various numerical methods. 

 books.google.com and we obtain the eigenvalues 4a _ 2 lhzr It, I —— sln —. h2 2 These
eigenvalues are all nonpositive, hence stability follows. ... eigenvectors are
damped by the method, in parallel with the smoothing property of the differential
operator and the ... 

 books.google.com Hence the ei gen functions and eigenvalues of (29) are (Ma «*.n(*, y) = sin mw
sin (3Ib) \** = [It can be shown that these ... In most cases, where the eigenvalues
of the differential operator obey a variational principle, the practical problem of ... 

 books.google.com Analytical and Numerical Methods, Second Edition Mark S. Gockenbach ... The
method of Fourier series: Differential operators, like d2/dx2, can have
eigenvalues and eigenfunctions; for example, 2 —2 [Sin(a)x)] I —a)2 sin(a)x). dx
The method ... 

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