A modified Euler method for dynamic analyses

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Abstract
A modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free‐vibrational responses of linear, undamped, single‐degree‐of‐freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.

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