General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence ...General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence of two families of characteristic lines along which initial stresses and discontinuities in them are transmitted intact far down to infinity.This is against our intuition and not verifiable by experimental findings. For the fundamental case of infinite uniform pressure on the upper surface,a comparison between solutions from equilibrium equations in Cartesian coordinates and from those in polar coordinates is carried out in details.The semi infinite characteristic lines in the former are bent up to exponential spirals with both ends on the upper surface in the latter.Thus,the transmission pattern from solution in polar coordinates comes closer to actual situation.However,in polar reference frame,the solution for distribution of stresses in particulate half space under surface strip pressure or so can then only be obtained from boundary value problem of second order partial differential equation.展开更多
Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg...Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Algorithm to prove the stability and convergence of the approximations.展开更多
In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condit...In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition. Optimal error bounds for this fully discrete scheme are obtained.展开更多
文摘General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence of two families of characteristic lines along which initial stresses and discontinuities in them are transmitted intact far down to infinity.This is against our intuition and not verifiable by experimental findings. For the fundamental case of infinite uniform pressure on the upper surface,a comparison between solutions from equilibrium equations in Cartesian coordinates and from those in polar coordinates is carried out in details.The semi infinite characteristic lines in the former are bent up to exponential spirals with both ends on the upper surface in the latter.Thus,the transmission pattern from solution in polar coordinates comes closer to actual situation.However,in polar reference frame,the solution for distribution of stresses in particulate half space under surface strip pressure or so can then only be obtained from boundary value problem of second order partial differential equation.
文摘Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Algorithm to prove the stability and convergence of the approximations.
文摘In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition. Optimal error bounds for this fully discrete scheme are obtained.
