A method of solving evolutionary problems based on the Laguerre step-by-step transform
In his previous publications, B.G. Mikhailenko proposed a method of solving dynamic problems of elasticity theory based on the Laguerre transform with respect to time. In this paper, we offer a modification of the given approach, which is in that the Laguerre transform is applied to a sequence of finite temporal intervals. The solution obtained at the end of one temporal interval is used as initial data for solving the problem at the next temporal interval. When implementing the approach in question, there arises a necessity of selecting the four parameters: the scale factor needed for approximating a solution by the Laguerre functions, the exponential coefficient of the weight function that is used for finding a solution on a finite temporal interval, the duration of this interval and the number of projections of the Laguerre transform. The way of selecting the above parameters for the stability of calculations is proposed. The effect of the applied method parameters on the accuracy of calculations when using difference schemes of second and fourth orders of approximation has been studied. It is shown that the use of such an approach makes possible to obtain a solution with a high accuracy on large temporal intervals.