A Method of Solving Evolutionary Problems Based on the Laguerre Step-by-Step Transform

In [1], Mikhailenko proposed a method of solving dynamic problems of elasticity theory. The method is based on the Laguerre transform with respect to time. In this paper, we propose a modification of this approach, applying the Laguerre transform to a sequence of finite time intervals. The solution obtained at the end of one time interval is used as initial data for solving the problem on the next time interval. To implement the approach, four parameters are chosen: a scale factor to approximate the solution by Laguerre functions, an exponential coefficient of a weight function that is used for finding a solution on a finite time interval, the duration of this interval, and the number of projections of the Laguerre transform. A way to find parameters that provide stability of calculations is proposed. The effect of the parameters on the accuracy of calculations when using second-and fourth-order difference schemes is studied. It is shown that the approach makes it possible to obtain a high-accuracy solution on large time intervals.