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Original Articles

Petrov-galerkin methods for nonlinear reaction-diffusion equations

Pages 123-145 | Received 21 Mar 1997, Published online: 30 Mar 2007

References

  • Arson , D. G. 1978 . A comparison method for stability analysis of nonlinear parabolic problems . SIAM Rev. , 20 : 245 – 264 .
  • Bebemes , J. W. and Schmitt , K. 1979 . On the existence of maximal and minimal solutions for parabolic partial differential equations . Pro. Amer. Math. Soc. , 73 : 211 – 218 .
  • Pao , C. V. 1985 . Monotone iterative methods for finite difference system of reaction-diffusion equations . Numer. Math. , 46 : 571 – 586 .
  • Pao , C. V. 1987 . Numerical methods of semilinear parabolic equations . SIAM J. Numer. Anal. , 24 : 24 – 35 .
  • Pao , C. V. 1993 . Positive solutions and dynamics of a finite difference reaction-diffusion system . Numer. Methods Partial Different. Eqs. , 9 : 285 – 311 .
  • Guo , Ben-yu and Mitchell , A. R. 1986 . Analysis of a non-linear difference scheme in reaction-diffusion . Numer. Math. , 49 : 511 – 527 .
  • Kuo , Pen-yu and Mitchell , A. R. 1983 . The stability of Petrov-Galerkin method for solving initial-boundary problem of convection-diffusion equation . Acta Math. Sinica , 26 : 54 – 64 .
  • Guo , Ben-yu and Miller , J. J. H . 1991 . “ Iterative and Petrov-Galerkin methods for a nonlinear two-point boundary problem with application to semiconductor devices ” . In Numerical Methods for Partial Differential Equations , Edited by: Lunan Yin and Guo Ben-yu . 23 – 34 . Singapore : World Scientific .
  • Guo , Ben-yu and Miller , J. J. H . 1992 . Iterative and Petrov-Galerkin methods for solving a system of one-dimensional nonlinear elliptic equations . Math. Comp. , 58 : 531 – 547 .
  • Boglaev , I. P. and Miller , J. J. H. 1988 . Petrov-Galerkin and Green's function methods for nonlinear boundary value problems with application to semiconductor devices . Pro. Roy. Irish Acad. Sect. , A88 : 153 – 168 .
  • Goel , N. S. , Maitra , S. C. and Montrel , E. W. 1971 . Nonlinear Models of Interacting Populations , New York : Academic .
  • Stakgold , I. and Payne , L. E. 1973 . “ Nonlinear problems in nuclear reactor analysis ” . In Nonlinear Problems in the Physical Sciences and Biology , Vol. 322 , New York : Springer-Verlag . Lecture Notes in Mathematics
  • Fife , P. C. 1979 . “ Lecture Notes in Biomathematics ” . In Mathematical Aspect of Reacting and Diffusing System , Vol. 28 , New York : Springer-Verlag .
  • Pao , C. V. 1992 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
  • Guo Ben-yu . 1988 . Difference Methods for Partial Differential Equations , Beijing : Science Press .
  • Collatz , L. 1964 . Funktionalanlysis und Numerische Mathematik , Berlin : Springer-Verlag .

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