Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Simple ECEM Algorithms Using Function Values Only

  • Kim, Philsu (Department of Mathematics, Kyungpook National University) ;
  • Kim, Sang Dong (Department of Mathematics, Kyungpook National University) ;
  • Lee, Eunjung (Department of Computational Science and Engineering, Yonsei University)
  • Received : 2013.11.05
  • Accepted : 2013.12.04
  • Published : 2013.12.23
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Abstract

In this paper, we improve the error corrected Euler method(ECEM) introduced in [11] by evaluating function values only at local nodes in each time interval. As a result, one can avoid computations of Jacobian matrices on each time interval so that the algorithms become simpler to implement in solving various class of time dependent differential equations numerically. The proposed ECEM formula resembles to the Runge-Kutta method in its representations but both methods have different characteristic properties.

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References

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