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Simple ECEM Algorithms Using Function Values Only

김상동|이은정|김필수
경북대학교 자연과학대학 수학과|2013.12|Kyungpook Mathematical Journal|제53권 제4호|pp. 573-591|DOI http://dx.doi.org/10.5666/KMJ.2013.53.4.573

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참고문헌

키워드

Runge-Kutta methodButcher’s tableError Corrected Euler Method
주제분류수학

초록

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.

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.

참고문헌 (24)

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