Explicit concomitance of implicit method to solve vibration equation

Abstract

It has been proven that the implicit method used to solve the vibration equation can be transformed into an explicit method, which is called the concomitant explicit method. The constant acceleration method’s concomitant explicit method was used as an example and is described in detail in this paper. The relationship between the implicit method and explicit method is defined, which provides some guidance about how to create a new explicit method that has high precision and computational efficiency.