Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

We develope a numerical method based on B-spline collocation method to solve linear Klein-Gordon equation. The proposed scheme is unconditionally stable. The results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. Easy and economical implementation is the strength of this approach.  

Consden, R., Gordon, A. H. & Martin, A. J. P. (1944). Biochem. J. 38, 224. Consden, R., Gordon, A. H. & Martin, A. J. P. (1945). Biochem. J. 39, xlvi. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946a). Biochem. J. 40, 33. Consden, R., Gordon, A. H. & Martin, A. J. P. (1946b). Biochem. J. 40, 580. Consden, R., Gordon, A. H., Martin, A. J. P. & Synge, R. L. M. (1947). Biochem. J. 41, 596. Mar...

G ordon Bell has had a long and varied career: early employee of Digital Equipment Corporation (DEC), designer of many of DEC’s PDP series of minicomputers, leader in computer science at the National Science Foundation, long-time proponent of the Computer History Museum in Mountain View, California, and creator and funder of the Gordon Bell Prize, which ACM awards for improvements to parallel a...

Thirty years ago, parallel computing was coming of age. A bitter battle began between stalwart vector computing supporters and advocates of various approaches to parallel computing. IBM skeptic Alan Karp, reacting to announcements of nCUBE’s 1024-microprocessor system and Thinking Machines’ 65,536-element array, made a public $100 wager that no one could get a parallel speedup of over 200 on re...