A note on solving the fourth order parabolic equation by the age method

References

• Crandall , S.H. 1954 . Numerical treatment of a fourth order partial differential equation . J. Assoc. Comp. Mach , 1 : 111 – 118 .
   Google Scholar
• Conte , S.D. and Royster , W.C. 1956 . Convergence of finite difference solutions to a solution of the equation of the vibrating rod . Proc. Amer. Math. Soc , 7 : 742 – 749 .
   Google Scholar
• Conte , S.D. 1957 . A stable implicit finite difference approximation to a fourth order parabolic equation . J. Assoc. Comp. Mach , 4 : 18 – 23 .
   Web of Science ®Google Scholar
• Albrecht , J. 1957 . Zum differenzenverfahren bei parabolischen differentialgleichungen . Z. Angew. Math and Mech , 37 ( 1-2 ) : 202 – 212 .
   Google Scholar
• Richtmyer , R.C. 1957 . “ Difference methods for initial value problems ” . In Interscience Tracts in Pure and Applied Mathematics , Vol. 4 , N.Y : Interscience Pubs .
   Google Scholar
• Evans , D.J. 1965 . A stable explicit method for the finite-difference solution of a fourth order parabolic partial differential equation . Comput. J , 8 : 280 – 287 .
   Web of Science ®Google Scholar
• Fairweather , G. and Gourlay , A.R. 1967 . Some stable difference approximations to a fourth-order parabolic partial differential equation . Maths, of Comp , 21 : 1 – 11 .
   Web of Science ®Google Scholar
• Lees , M. 1961 . Alternating direction and semi-explicit difference methods for parabolic partial differential equations . Numer. Math , 3 : 398 – 412 .
   Google Scholar
• Douglas , J. 1956 . The solution of the diffusion equation by a high order correct difference equation . J Math. Phys , 35 : 145 – 151 .
   Google Scholar
• Evans , D.J. and Yousif , W.S. 1988 . The solution of two point boundary value problems by the alternating group explicit (AGE) method . SIAM J. Set Stat. Comput , 9 ( 3 ) : 474 – 484 .
   Web of Science ®Google Scholar