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Original Articles

Linearly implicit generalized trapezoidal formulas for nonlinear differential equations

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Pages 345-359 | Received 07 May 1999, Published online: 19 Mar 2007

References

  • Beam , R. M. and Warming , R. F. 1978 . An implicit factored scheme for the compressible Navier-Stokes equations . AIAA J. , 16 : 393 – 402 .
  • 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 .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1996 . A class of generalized trapezoidal formulas for the numerical integration of y′ = f(x,y) . Intern. J. Computer Math. , 62 : 131 – 142 .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1999 . Generalized trapezoidal formulas for parabolic equations . Intern. J. Computer Math. , 70 : 429 – 443 .
  • Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1999 . Generalized trapezoidal formulas for convection-diffusion equations . Intern. J. Computer Math. , to appear
  • Debnath , L. 1997 . Nonlinear Partial Differential Equations for Scientists and Engineers , Boston : Birkhäuser .
  • Finckenstein , K. V. 1987 . Difference methods for quasilinear parabolic systems from plasma physics . Numer. Meth. PDEs , 3 : 289 – 311 .
  • Le Roux , M.-N. 1994 . Semidiscretization in time of nonlinear parabolic equations with blowup of the solution . SIAM J. Numer. Anal. , 31 : 170 – 195 .
  • Lubich , Ch. and Ostermann , A. 1995 . Linearly implicit time discretization of non-linear parabolic equations . IMA J. Numer. Anal. , 15 : 555 – 583 .
  • Meyer-Spasche , R. 1998 . Difference schemes of optimum degree of implicitness for a family of simple ODEs with blow-up solutions . J. Comput. Appl. Math. , 97 : 137 – 152 .
  • O′ Malley , R. E. Jr . 1997 . Thinking About Ordinary Differential Equations , Cambridge : Cambridge Univ. Press .
  • Wouwer , A. V. , Saucez , P. and Schiesser , W. E. 1998 . Some user-oriented comparisons of adaptive grid methods for partial different equations in one space dimension . Appl. Numer. Math. , 26 : 49 – 62 .

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