41
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A monotone weighted average method for a non-linear reaction–diffusion problem

Pages 1017-1031 | Received 19 Oct 2004, Published online: 25 Jan 2007

References

  • Ladyženskaja , O. A. , Solonnikov , V. A. and Ural’ceva , N. N. 1968 . Linear and Quasi-Linear Equations of Parabolic Type , New York : Academic Press .
  • Boglaev , I. P. 1990 . Numerical solution of a quasilinear parabolic equation with a boundary layer . Computational Mathematics and Mathematical Physics , 30 : 55 – 63 .
  • Pao , C. V. 1985 . Monotone iterative methods for finite difference system of reaction–diffusion equations . Numerische Mathematik , 46 : 571 – 586 .
  • Pao , C. V. 1995 . Finite difference reaction diffusion equations with nonlinear boundary conditions . Numerical Methods for Partial Differential Equations , 11 : 355 – 374 .
  • Boglaev , I. P. 2004 . Monotone iterative algorithms for a nonlinear singularly perturbed parabolic problem . Journal of Computational and Applied Mathematics , 172 : 313 – 335 .
  • Samarskii , A. 2001 . The Theory of Difference Schemes , New York : Marcel Dekker .
  • Morton , K. W. and Mayers , D. F. 1995 . Numerical Solution of Partial Differential Equations , New York : Cambridge University Press .
  • Crank , J. and Nicolson , P. 1947 . A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type . Proceedings of the Cambridge Philosophical Society , 43 : 50 – 67 .
  • Boglaev , I. P. 2004 . “ A monotone weighted average method for a nonlinear singularly perturbed reaction–diffusion problem ” . Reports in Mathematics No. 11 New Zealand : Institute of Fundamental Sciences, Massey University .
  • Miller , J. J.H. , O’Riordan , E. and Shishkin , G. I. 1996 . Fitted Numerical Methods for Singular Perturbation Problems , Singapore : World Scientific .
  • Saad , Y. and Schultz , M. H. 1986 . GMRES: a generalized minimal residual method for solving nonsymmetric linear systems . SIAM Journal on Scientific and Statistical Computing , 7 : 856 – 869 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.