جستجوی مقالات مرتبط با کلیدواژه « crank » در نشریات گروه « علوم »

In this paper, the quintic B-spline collocation scheme is employed to approximate numerical solution of the KdV-like Rosenau equation. This scheme is based on the Crank-Nicolson formulation for time integration and quintic B-spline functions for space integration. The unconditional stability of the present method is proved using Von- Neumann approach. Since we do not know the exact solution of the nonlinear KdV-like Rosenau equation, a comparison between the numerical solutions on a coarse mesh and those on a refine mesh is made to show the efficiency of discussed method.

A 2-D heat conduction model has been solved by using the Adomian Decomposition Method to predict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source. The laser source may operate in a continuous wave (CW) mode or repeated pulse (RP) mode and may have arbitrary, spatial and temporal profiles. A generalized solution containing five-terms approximation of a rapidly convergent series is obtained. The solution is then applied to some special cases of practical interest, such as laser irradiation of sandstones and limestones. Laser drilling of geologic formations is being considered by the petroleum industry in the foreseeable future. The 2-D transient temperature distribution is presented in a graphical form and discussed. A comparison between the results obtained from the Adomian method and those obtained numerically by using the Crank-Nicholson method is also presented.