This paper provides an inverse formula freed of determinant expressions for a general tridiagonal matrix. This is viewed as an alternative version of the Usmani formula, which easily tends to blow up computationally. We discuss a number of different viewpoints regarding the proposed and Usmani’s formulas, such as the proof method and the meaning of included terms, although our formula itself ma...

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotiv...

mathematical simulation of flow toward drains is an important and indispensable stage in drainage design and management. many related models have been developed, but most of them simulate the saturated flow toward drains without a due consideration of the unsaturated zone. in this study, the two dimensional differential equation governing saturated and unsaturated flow in porous media is numeri...

The present study concentrates on the effects of viscous dissipation in laminar forced convection. A power law fluid rheology model is applied and the effect of heat conduction in the axial direction is considered negligible. The physical properties are considered constant. Assuming fully developed velocity profile, the development of the temperature profile and its asymptotic behavior are inve...

The present paper is devoted to the application of the space transformation techniques for solving linear programming problems. By using a surjective mapping the original constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem the stable version of the gradient-projection and Newton's methods ar...

Using a help system to make easier the CAS-user connection, we propose the problem of solving the equation of diffusion with variable coefficients. We transform the problem at the Laplace domain and we use the Bromwich integral and the residue theorem in order to do the inverse Laplace transform and then explicit solution is obtained.

advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

This paper gives a generalization of the Pseudo-Laplace transform. In the special cases of semirings, the pseudo-exchange formula is proved. Also, for these semirings the forms of the Pseudo-Laplace transform and inverse operator are given. The results can be applied in dynamical programming for finding the maximum and minimum of the utility functions. AMS Mathematics Subject Classification (19...

We present a form of the discrete dipole approximation for electromagnetic scattering computations in time domain. We show that the introduction of complex frequencies, through the Laplace transform, significantly improves the computation time. We also show that the Laplace transform and its inverse can be combined to extract the field inside a scatterer at a real resonance frequency.

The distributed relaxation method for the Stokes problem has been advertised as an adequate change of variables that leads to a lower triangular systemwith Laplace operators on the main diagonal for which multigrid methods are very efficient. We show that under high regularity of the Laplacian, the transformed system admits almost block-lower triangular form.We analyze the distributed relaxatio...