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Based on a one-dimensional thermal consolidation formulation of saturated soil, problems of one-dimensional thermal consolidation of saturated soil under different thermal loading were investigated. The analytical solutions of excess pore water pressure, temperature increase and the settlement of ground are derived by the method of partial differential equation. The one-dimensional thermal consolidation...
Singularly perturbed ordinary differential equation with two small parameters is considered. Firstly, the solution is decomposed into the smooth component and the singular component. The upper bounds of the smooth component and the singular component are studied. Secondly, the traditional Shishkin's scheme is presented and it is proved to be uniformly convergent with respect to the small parameter...
Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer...
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