Iranian Journal of science and Technology (A: Siences)
Volume:30 Issue: 2, Summer 2006

Finite and boundary element methods have been used by many authors to solve mathematical physics problems. However, the coupling of these two methods happens to be more efficient as it combines their merits. In this paper, the mathematical analysis of the coupling of finite and boundary element methods for the Helmholtz equation is presented.

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.

In this paper, the stability and boundedness of solutions of a second order nonlinear vector differential equation are investigated. Our results include and improve some well-known results in the relevant literature.

In this paper, we obtain two intrinsic integral inequalities of Hessian manifolds.