Numerical Solution Of One-dimensional Problem Research Articles

Cylindrical shear waves in soil around underground pipelines

A method of numerical solution of one-dimensional problem of cylindrical shear wave propagation in an elastic and elastic-plastic soil is developed in the article using the finite difference method. The numerical results obtained are presented in the form of graphs. From the results obtained, the attenuation of the parameters (shear stress, shear strain, and angular velocity) of cylindrical wave propagation with distance in an elastic and elastic-plastic soil was determined. The attenuation of waves with distance is justified by the dissipation of strain energy on the expanding cylindrical soil layer. In the case of load exceeding the elastic limit, plastic strains occur in soil near the point of load application. The boundaries of elastic-plastic strain of soil are determined.

Численное решение одномерной задачи фильтрации с учетом суффозионных процессов

Численное решение одномерной задачи фильтрации с учетом суффозионных процессов

On the application of adaptive grids to the numerical solution of one-dimensional problems in the shallow-water theory

On the application of adaptive grids to the numerical solution of one-dimensional problems in the shallow-water theory

Asymptotic error expansions for numerical solutions of one-dimensional problems with singularities

A systematic analysis is given on asymptotic error expansions for numerical solutions of one-dimensional problems whose solutions are singular. Numerical examples show a great improvement on the accuracy of numerical solutions by using the Richardson extrapolation technique.