References
- Albrecht , J. 1957 . Zum Differenzenverfahren bei parabolischen Differentiat gleichungen . Z. Angew. Math. Mech. , 37 : 202 – 212 .
- Andrade , C. and Mc Kee , S. 1977 . High accuracy A. D. I. methods for fourth order parabolic equations with variable coefficients . Internat. J. Comput. Appl. Math. , 3 : 11 – 14 .
- Collatz , L. 1951 . Zur Stabilitat des Differenzenverfahrens bei der Stabschwingungs-gleichung . Z. Angew. Math. Mech. , 31 : 392 – 393 .
- Conte , S. D. 1957 . A stable implicit finite difference approximation to a fourth order parabolic equation . J. Assoc. Comp. Mach. , 4 : 210 – 212 .
- Conte , S. D. and Royster , W. C. 1956 . Convergence of finite difference solutions to a solution of the equation of a vibrating rod . Proc. Amer. Math. Soc. , 7 : 742 – 749 .
- Crandell , S. H. 1954 . Numerical treatment of a fourth order partial differential equation . J. Assoc. Comp. Mach. , 1 : 111 – 118 .
- Douglas , J. Jr. 1956 . The solution of the diffusion equation by a high order correct difference equation . J. Math. Phys. , 35 : 145 – 151 .
- Du Fort , E. C. and Frankel , S. P. 1953 . Stability conditions in the numerical treatment of parabolic partial differential equations . MTAC , 7 : 135 – 152 .
- Evans , D. J. 1965 . A stable explicit method for the finite difference solution of fourth order parabolic partial differential equations . Comp. J. , 8 : 280 – 287 .
- Fairweather , G. and Gourlay , A. R. 1967 . Some stable difference approximations to a fourth order parabolic partial differential equation . Comp. Math. , 21 : 1 – 11 .
- Gorman , D. J. 1975 . Free Vibration Analysis of Beams and Shafts , New York : John Wiley & Sons .
- Lees , M. 1961 . Alternating direction and semi-explicit difference methods for parabolic partial differential equations . Numer. Math. , 3 : 24 – 47 .
- Richtmyer , R. D. 1957 . Difference Methods for Initial Value Problems , New York : Interscience .
- Twizell , E. H. 1984 . Computational Methods for Partial Differential Equations , 276 – 276 . Chichester : Ellis Horwood/John Wiley & Sons .
- Twizell , E. H. and Khaliq , A. Q. M. 1983 . A difference scheme with high accuracy in time for fourth-order parabolic equations . Comp. Meth. Appl. Mech. Engineering , 41 : 91 – 104 .