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The paper discusses the development of an algorithm for solving two-dimensional boundary value problems for a nonlinear partial parabolic differential equation with degeneration. The nonlinearity of the equation is dictated by a power law between the heat conductivity coefficient and temperature. The solution algorithm is based on the boundary element method with the application of the dual reciprocity method. The solution accuracy is analyzed for the discussed type of problems, with the application of different systems of radial basis functions. The most suitable system of functions and their parameters are determined. [ABSTRACT FROM AUTHOR]

The paper deals with the development of algorithms for solving nonlinear problems of heat conduction in bodies consisting of layered metal composites. The nonlinearity of the problems is governed by the temperature dependence of the heat conductivity coefficients of the composite layer materials. Mathematical models and solution algorithms based on the boundary element method have been constructed for one-dimensional cases of heat distribution. [ABSTRACT FROM AUTHOR]

The present paper is dedicated to numerical solving of three dimensional boundary-value problems in poroelastic formulation. Boundary element method and boundary integral equation method are applied to obtain Laplace domain solution of boundary-value problem. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. A problem of the three-dimensional poroelastic prismatic solid clamped at one end, and subjected to uniaxial and uniform impact loading at another is considered. [ABSTRACT FROM AUTHOR]