Higher-order explicit time integration methods for numerical analyses of structural dynamics

In this article, third- and fourth-order accurate explicit time integration methods are developed for effective analyses of various linear and nonlinear dynamic problems stated by second-order ordinary differential equations in time. Two sets of the new methods are developed by employing the collocation approach in the time domain. To remedy some shortcomings of using the explicit Runge-Kutta methods for second-order ordinary differential equations in time, the new methods are designed to introduce small period and damping errors in the important low-frequency range. For linear cases, the explicitness of the new methods is not affected by the presence of non-diagonal damping matrix. For nonlinear cases, the new methods can handle velocity dependent problems explicitly without decreasing order of accuracy. The new methods do not have any undetermined algorithmic parameters. Improved numerical solutions are obtained when they are applied to various linear and nonlinear problems.