Hybrid method of space-time and Houbolt methods for solving linear time-dependent problems

Abstract

A hybrid method, through coupling the space-time method based on the polynomial particular solutions method and the Houbolt method, has been proposed to solve time-dependent problems. The main attractions of the proposed hybrid method are its novelty and high efficiency. Because the Houbolt method is a four level time difference method, the first three time steps initial values have to be calculated in advance. In general, these initial values are computed by Euler method. Consequently, the serious initial bump appears. In the current work, the difficulty of handling the multiple initial values in the solution procedure of the Houbolt method has been alleviated by adopting the space-time method at the beginning procedure, then by following the traditional Houbolt method. Therefore, the proposed hybrid method preserves the advantages of both the space-time method and the Houbolt method. The efficiency of our proposed method is analyzed through three numerical examples in two-dimensional space on regular and irregular domains.