A time integration algorithm for linear transient analysis based on the reproducing kernel method

In this paper a new algorithm based on the reproducing kernel method is presented for linear transient analysis using very large time steps. In the conventional time integration methods, the required accuracy is always achieved by either decreasing the size of time steps or increasing the order of approximations. The proposed method, however, does not require a restriction on the size of the time step. The required approximating functions for integration of governing equations are determined using the concept of reproduction of the solution within each time step. A recurrence relationship is obtained through solving the governing equation by the point collocation based reproducing kernel method within the time step. In collocation points, the values of external excitation can be obtained either through the approximation between the values at the beginning and the end of each time step or assigning the exact values of the external force. Hence, one advantage of this new method is the independency of the sampling rates of external excitation from the size of the time step. The proposed method is applied for solving first and second order differential equations, and advantages of the method are illustrated through a number of numerical examples.