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Developments in the NAG library software for parabolic equations

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Scientific Software Systems

Abstract

The NAG Library parabolic partial differential equation (p.d.e.) sub-chapter D03P has recently been revised to make use of the successful SPRINT Leeds University/Shell Research Software and so offers a range of different space discretization methods that can be applied to a common problem class of parabolic-elliptic systems of p.d.e.s with coupled differential-algebraic equations. Three significant advances over the existing software in D03P are the wide class of problems that can be solved, the spatial remeshing routines that are available and the modular structure which allows a wide range of NAG time integration and linear algebra routines to be used with all the spatial discretization routines. The improvements that these new routines offer over the existing D03P routines are illustrated by a number of example problems. The future requirements of software in this area are considered.

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References

  • Berzins, M. and Furzeland, R.M. (1985), A type-insensitive method for the solution of stiff and non-stiff differential equations. Leeds University, Department of Computer Studies, Report No 204

    Google Scholar 

  • Berzins, M. (1986), A C1 interpolant for codes based upon backward differentiation formulae. Applied Numerical Analysis, Vol 2 pp 109–118

    Google Scholar 

  • Berzins, M. and Furzeland, R.M. (1986), A user’s manual for SPRINT — a versatile software package for solving systems of algebraic ordinary and partial differential equations: part 2 partial differential equations, TNER. 86.093, Thornton Research Centre, Chester

    Google Scholar 

  • Berzins, M. and Dew, P.M. (1987), CO Chebyshev methods for parabolic p.d.e.s. I.M.A. Journal of Numerical Analysis, Vol 7, pp 15–37

    Article  Google Scholar 

  • Berzins, M. Brankin, R. and Gladwell, I. (1987), The design of stiff integrators in the NAG library, University of Manchester, Department of Mathematics Report, 7, see also SIGNUM Newsletter (1988)

    Google Scholar 

  • Berzins, M., Dew, P.M. and Furzeland, R.M. (1988), Developing software for time-dependent problems using the method of lines and differential algebraic integrators, in press with Appl. Num. Math.

    Google Scholar 

  • Dew, P.M. and Walsh, J.E. (1981) A set of library routines for solving parabolic equations in one space variable. ACM Trans, on Math. Soft., Vol 7, No 3, pp 295–314

    Article  Google Scholar 

  • Furzeland, R.M. (1985), The construction of adaptive space meshes, TNER,85,022, Shell Research Ltd., Thornton Research Centre, P.O. Box 1, Chester CH1 3SH

    Google Scholar 

  • Gaffney, P. (1982), Using the method of lines technique to solve boundary value p.d.e.s. In ‘Scientific Computation’, ed R. Stepleman, IMACS/North Holland.

    Google Scholar 

  • Grosh, C. and Orszag, S.A. (1977), Numerical solution of problems in unbounded regions: co-ordinate transforms. Journal of Computational Physics, Vol 25, pp 273–296

    Article  Google Scholar 

  • Keller, H.B. (1970), A new difference scheme for parabolic equations, Numerical Solution of Partial Differential Equations, Vol 2, (J. Bramble, ed) Academic Press, New York

    Google Scholar 

  • Schryer, N.L. (1984), Partial differential equations in one space variable, Computing Science Technical Report No 115, 1984, AT and T Laboratories, Murray Hill, New Jersey 07974

    Google Scholar 

  • Skeel, R. D. and Berzins, M. (1987), Spatial discretization methods for parabolic p.d.e.s, paper submitted to SIAM Journ. of Sci. and Stat. Comp.

    Google Scholar 

  • Zaturska, N.B., Drazin, P.G. and Banks, W.H.H. (1988), On the flow of a viscous fluid driven along a channel by suction at porous walls. Fluid Dynamics Research, Vol 4, 1988, in press

    Google Scholar 

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© 1990 Chapman and Hall

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Berzins, M. (1990). Developments in the NAG library software for parabolic equations. In: Mason, J.C., Cox, M.G. (eds) Scientific Software Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0841-3_4

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  • DOI: https://doi.org/10.1007/978-94-009-0841-3_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6865-9

  • Online ISBN: 978-94-009-0841-3

  • eBook Packages: Springer Book Archive

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