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Multi-level adaptive solutions to initial-value problems

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Abstract

A multigrid algorithm is developed for solving the one-dimensional initial boundary value problems. The numerical solutions of linear and nonlinear Burgers’ equation for various initial conditions are studied. The stability conditions are derived by Von-Neumann analysis. Numerical results are presented.

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References

  1. A. Brandt,Multi-Level Adaptive Solution to Boundary-Value Problem, Math. Comp.31 (1977), 333–390.

    Article  MATH  MathSciNet  Google Scholar 

  2. C.I. Goldstein,Analysis and Application of Multigrid Preconditioners for Singularyly Perturbed Boundary Value Problems, Siam, Numer.Anal.26 (1989), 1090–1123.

    Article  MATH  Google Scholar 

  3. C. Dennis Jespersen,Multigrid Method for Partial Differential equations, Studies in Numerical Analysis24 (1984).

  4. W. Hachbusch and U. Trottenberg,Multigrid Methods: Special Topics and Applications, Bonn, October 1–4., 1990.

  5. K. Stuben and U. Trottenberg,Multigrid Methods Fundamental Algorithms Model Problem Analysis and Applications, GMD. Studien Nr 96, 1984.

  6. P. Wesseling,An Introduction to Multigrid Methods, (John Wiley & Sons New York), 1992.

    MATH  Google Scholar 

  7. A. Hassen Nasr, M. Osama Elgiar and M. Fatema Hassan,The Relaxation Schemes For The Two Dimensional Anisotropic Partial Differential Equations Using Multigrid Method, Conf. for Stat., Comp. Scie., Scient & Social Appl., Cairo 17–22 April (1995).

  8. G.D. Cole,On Quasilinear Prabolic Equation Occuring in Aerodynamics, Quarterly of Applied Mathematic9 (1951), 225–236.

    MATH  MathSciNet  Google Scholar 

  9. J. Bugers,A Mathematical Model Illstrating the Theory of Turbulence, Advances in Applied Mechanics Academic Press London (1948), 171–199.

    Google Scholar 

  10. J. Cadwell, P. Wanless and A.E. Cook,A Finite Element Approach to Burgers’ Equation, Appl. Math. Modelling5 (1981), 189–193.

    Article  MathSciNet  Google Scholar 

  11. B.M. Herbst, S.W. Schoombie and A.R. Mitchell,A Moving Petrov-Galerkin Method for Transport Equations, Int.J.for Num.Meth. in Enging.18 (1982), 1321–1336.

    Article  MATH  MathSciNet  Google Scholar 

  12. L.R.T. Gardner, G.A. Gardner and A.H.A. Ali,A method of lines solutions for Burgers’ equation, Computational Mechanics (1991), 1555–1561.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Elmenia University, Egypt

    A. B. Shamardan

  2. Department of Mathematics Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    Y. M. Abo Essa

Authors
  1. A. B. Shamardan
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  2. Y. M. Abo Essa
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Shamardan, A.B., Essa, Y.M.A. Multi-level adaptive solutions to initial-value problems. Korean J. Comput. & Appl. Math 7, 215–222 (2000). https://doi.org/10.1007/BF03009939

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  • DOI: https://doi.org/10.1007/BF03009939

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