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Original Articles

A new L-stable Simpson-type rule for the diffusion equation

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Pages 601-607 | Received 23 Aug 2004, Published online: 20 Aug 2006

References

  • Crank , J. and Nicolson , P. 1947 . A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type . Proc. Camb. Philos. Soc. , 43 : 50 – 67 .
  • Mitchell , A. R. and Griffiths , D. F. 1980 . The Finite Difference Method in Partial Differential Equations , New York : John Wiley .
  • Morton , K. W. and Mayers , D. F. 1994 . Numerical Solution of Partial Differential Equations , Cambridge : Cambridge University Press .
  • Smith , G. D. 1978 . Numerical Solution of Partial Differential Equations: Finite Difference Methods , 2nd edn , Oxford : Oxford University Press .
  • Thomas , J. W. 1995 . Numerical Partial Differential Equations: Finite Difference Methods , New York : Springer-Verlag .
  • Richtmyer , R. D. and Morton , K. W. 1967 . Difference Methods for Initial-Value Problems , New York : Wiley-Interscience .
  • Lawson , J. D. and Morris , J. L. 1978 . The extrapolation of first order methods for parabolic partial differential equations I . SIAM J. Numer. Anal. , 15 : 1212 – 1224 .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1999 . Generalized trapezoidal formulas for parabolic equations . Int. J. Comput. Math. , 70 : 429 – 443 .
  • Lambert , J. D. 1991 . Numerical Methods for Ordinary Differential Systems , New York : John Wiley .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Al-Sahhar , M. S. 1994 . Stabilized fourth order extended methods for the numerical solution of ODEs . Int. J. Comput. Math. , 52 : 99 – 107 .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1996 . A class of generalized trapezoidal formulas for the numerical integration of . Int. J. Comput. Math. , 62 : 131 – 142 .
  • Berzins , M. , Capon , P. J. and Jimack , P. K. 1998 . On spatial adaptivity and interpolation when using the method of lines . Appl. Numer. Math. , 26 : 117 – 133 .

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