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Direct computational approaches to a magnetohydrodynamic model system

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Summary

The magnetohydrodynamic model system is integrated numerically as an initial-value problem. The system is integrated using two-different numerical methods. The first uses a special finite difference scheme introduced byBellman. The second makes use of the classical method of converting a partial differential equation into an infinite system of ordinary differential equations. The formulation for each computational scheme is discussed and numerical example presented.

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References

  1. Burgers, J. M.: Advances in Applied Mechanics. Vol. 1, p. 171. New York: Academic Press, Inc. 1948.

    Google Scholar 

  2. Thomas, J. H.: Numerical Experiments on a Model System for Magnetohydrodynamic Turbulence. Phys. Fluids11, 1245 (1968).

    Article  MATH  Google Scholar 

  3. Bellman, R. E., R. E. Klaba, andB. Kotkin: On a New Approach to the Computational Solution of Partial Differential Equations. Proc. Nat. Acad. Sci. U. S.48, 1325 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  4. Bellman, R. E., I. Cherry, andC. M. Wing: A Note on the Numerical Integration of a Class of Nonlinear Hyperbolic Equations. Quart. Appl. Math.16, 181 (1958).

    MathSciNet  MATH  Google Scholar 

  5. Bellman, R. E., S. P. Azen, andJ. M. Richardson: On New and Direct Computational Approaches to Some Mathematical Models of Turbulence. Quart. Appl. Math.23, 55 (1965).

    MathSciNet  MATH  Google Scholar 

  6. Bellman, R. E.: On the Existence and Boundedness of Solution of Nonlinear Partial Differential Equation of Parabolic Type. Trans. Am. Math. Soc.64, 21 (1948).

    Article  MATH  Google Scholar 

  7. Ralson, A., andH. S. Wilf: Mathematical Method of Digital Computer, p. 95. New York: Wiley. 1960.

    Google Scholar 

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Authors and Affiliations

  1. School of Engineering and Applied Science, University of California, 90024, Los Angeles, CA, USA

    Dah-Teng Jeng

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  1. Dah-Teng Jeng
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Jeng, DT. Direct computational approaches to a magnetohydrodynamic model system. Computing 7, 1–12 (1971). https://doi.org/10.1007/BF02279936

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  • DOI: https://doi.org/10.1007/BF02279936

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