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An implicit one-step method of high-order accuracy for the numerical integration of ordinary differential equations

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Abstract

For a differential equationdx/dt=f(t, x) withf t (t, x),f x (t, x) computable, the author presents a new one-step method of high-order accuracy. A rule of controlling the mesh size is given and the method is compared with the Runge-Kutta method in two numerical examples.

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References

  1. Urabe, M.: Convergence of numerical iteration in solution of equations. J. Sci. Hiroshima Univ. Ser. A,19, 479–489 (1956).

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  2. ——: Error estimation in numerical solution of equations by iteration process. J. Sci. Hiroshima Univ. Ser. A-I,26, 77–91 (1962).

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Kyoto, Japan

    Minoru Urabe

Authors
  1. Minoru Urabe
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Dedicated to Professor Dr. Dr. h. c. L. Collatz for his 60th birthday

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Urabe, M. An implicit one-step method of high-order accuracy for the numerical integration of ordinary differential equations. Numer. Math. 15, 151–164 (1970). https://doi.org/10.1007/BF02165379

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  • DOI: https://doi.org/10.1007/BF02165379

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