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Some higher order methods for computing eigenvalues of two-point boundary value problems

โœ Scribed by Usmani, Riaz A. ;Agarwal, Ravi P.

Publisher
Wiley (John Wiley & Sons)
Year
1987
Tongue
English
Weight
215 KB
Volume
3
Category
Article
ISSN
0748-8025

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โœฆ Synopsis

We present new finite difference methods of order at most O(hh) for computing eigenvalues of two-point boundary value problems. Our methods lead to generalized seven-band matrix eigenvalue problems. Some typical boundary value problems are treated numerically and these numerical results are summarized in order to demonstrate the practical usefulness of our algorithms.

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A higher-order accurate Petrov-Galerkin
A higher-order accurate Petrov-Galerkin finite-element method for elliptic boundary-value problems
โœ MacKinnon, R. J. ;Johnson, R. W. ;Langerman, M. A. ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Wiley (John Wiley & Sons) ๐ŸŒ English โš– 311 KB ๐Ÿ‘ 2 views

We formulate a higher-order (superconvergent) Petrov-Galerkin method by determining, using a finitedifference approximation, the optimal selection of quadratic and cubic modifications to the standard linear test function for bilinear elements. Application of this method to linear elliptic problems r