Skip to main content

On the numerical solution of linear mixed problems

  • Fluid Mechanics
  • Conference paper
  • First Online:
Book cover Computing Methods in Applied Sciences

Part of the book series: Lecture Notes in Physics ((LNP,volume 58))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. K. Aziz and S. Leventhal, “On Numerical Solutions of Equations of Hyperbolic Elliptic Type”,(to appear).

    Google Scholar 

  2. A. K. Aziz, G. Fix and S. Leventhal, “Optimal Error Estimates for Space-Time Galerkin Method”,(to appear).

    Google Scholar 

  3. —, “Difference Schemes Generated by a Space-Time Galerkin Method”, (to appear).

    Google Scholar 

  4. S. Bergman, “Methods or Determination and Computation of Flow Patterns of a Compressible Fluid”, NACAT Technical Note No. 1018 (1946).

    Google Scholar 

  5. —, “Operator Methods in the Theory of Compressible Fluids”, Proceedings of Symposia in Appl. Math., 1 (1949), 1–18.

    Google Scholar 

  6. L. Bers, “Mathematical Aspects of Subsonic and Transonic-Gas Dynamics”. Surveys in Appl. Math. III (1958).

    Google Scholar 

  7. A. V. Bitsadze, Equations of the Mixed Type, The MacMillan Company, New York (1964).

    MATH  Google Scholar 

  8. C. K. Chu, “Type-Insensitive Difference Schemes”, Ph.D. Thesis, New York University (1959).

    Google Scholar 

  9. A. Filippov, “On Difference Methods for the Solution of the Tricomi Problem”, Izv. Akad. Nauk SSR. Ser. Mat., 21 (1957), 73–88.

    MATH  Google Scholar 

  10. K. O. Friedrichs, “Symmetric Positive Linear Differential Equations”, Comm. Pure Appl. Math., 11 (1958), 333–418.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Guderley and H. Yoshihara, “The Flow Over a Wedge Profile at Mach Number 1”, Journal of the Aeronautical Sciences, 17 (1950), 723–735.

    MATH  MathSciNet  Google Scholar 

  12. —, “Two-dimensional Unsymmetric Patterns at Mach Number 1”, Journal of the Aeronautical Sciences, 20 (1953), 756–768.

    Google Scholar 

  13. Z. I. Halilov, “Solutions of a Problem for an Equation of Mixed Type by the Method of Grids”, Akad. Nauk. Azerbaidzanskogo SSR, Trudy Inst. Fiz.-Mat., 6 (1953), 5–13.

    MathSciNet  Google Scholar 

  14. —, “Solution of a Problem for an Equation of Mixed Type by the Method of Nets”, Dokl. Adad. Nauk. Azerbaidzanskogo SSR, 9 (1953), 189–194.

    MathSciNet  Google Scholar 

  15. A. Jameson, “Numerical Solution of Nonlinear Partial Differential Equations of Mixed Type”, Numerical Solution of Partial Differential Equations-III, (B. Hubbard, ed.), Academic Press 1975.

    Google Scholar 

  16. G. D. Karatoprakliev, “Equation of Mixed Type and Degenerate Hyperbolic Equations in Multidimensional Regions”, Differential’nye Uravnenija, No.1. 8 (1973), 55–67.

    MathSciNet  Google Scholar 

  17. B. G. Karmanov, “On a Boundary Value Problem for an Equation of Mixed Types”, Doklady, 95 (1954), 439–442.

    MATH  MathSciNet  Google Scholar 

  18. T. Katsanis, “Numerical Solution of Symmetric Positive Differential Equations”, Math. Comp. 22 (1968), 763–783.

    Article  MATH  MathSciNet  Google Scholar 

  19. —, “Numerical Solution of Tricomi Equation Using Theory of Symmetric Positive Differential Equations”, SIAM J. Numer. Anal. No. 2 (1969), 236–253.

    Google Scholar 

  20. O. A. Ladyzenskaya, “On One Method for Approximating the Solution to the Lavrent’ev-Bitsdze Problem”, Uspehi Math. Nank, 9, 4. (1954), 187–189.

    MathSciNet  Google Scholar 

  21. P. D. Lax and R. S. Phillips, “Local Boundary Conditions for Dissipative Symmetric Linear Differential Operators”, Comm. Pure Appl. Math. 13 (1960), 427–455.

    Article  MATH  MathSciNet  Google Scholar 

  22. P. Lesaint, “Finite Element Methods for Symmetric Hyperbolic Equations”, Numer. Math. 21 (1973), 244–255.

    Article  MATH  MathSciNet  Google Scholar 

  23. D. Levey, “A Numerical Scheme for Solving a Boundary Value Problem for the Tricomi Equation”, Ph.D. Thesis, New York University (1957).

    Google Scholar 

  24. C. Morawetz, “A Uniqueness Theorem for Frankl’s Problem”, Comm. Pure Appl. Math. 7 (1954), 697–703.

    Article  MATH  MathSciNet  Google Scholar 

  25. —, “A Weak Solution for a System of Equations of Elliptic-Hyperbolic Type”, Comm. Pure Appl. Math., 11 (1958), 315–331.

    Article  MATH  MathSciNet  Google Scholar 

  26. E. M. Murman, and J. D. Cole, “Calculation of Plane Steady Transonic Flows”, AIAA J. 9 (1971), 114–121.

    Article  MATH  Google Scholar 

  27. H. Ogawa, “On Difference Methods for the Solution of a Tricomi Problem”, Trans. Amer. Math. Soc., 100 (1961), 404–424.

    Article  MATH  MathSciNet  Google Scholar 

  28. L. V. Ovsiannikov, “Concerning the Tricomi Problem for One Class of Generalized Solutions of the Euler-Darboux Equation”, Doklady, 91 (1953), 457–460.

    Google Scholar 

  29. S. Schecter, “Quasi-Tridiagonal Matrices and Type-Insensitive Difference Equations” Quart. Appl. 18 (1960), 285–295.

    Google Scholar 

  30. J. A. Trangenstein, “A Finite Element Method for the Tricomi Problem in the Elliptic Region”, Ph.D. Thesis, Cornell University (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

R. Glowinski J. L. Lions

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag

About this paper

Cite this paper

Aziz, A.K., Fix, G., Leventhal, S. (1976). On the numerical solution of linear mixed problems. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences. Lecture Notes in Physics, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120609

Download citation

  • DOI: https://doi.org/10.1007/BFb0120609

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08003-9

  • Online ISBN: 978-3-540-37550-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics