This paper is devoted to studying the approximate solution of singular integral equations by means of Chebyshev polynomials. Some examples are presented to illustrate the method.
In This paper, a software has been designed to perform the alternating direction implicit, ADI, method for the case of two dimensional flow represented by Poisson's equation. A square mesh with varying mesh size has been adopted. The results came out very much complying with the analytical solutions asserting the rigour of the software.
The paper is concerned with the applicability of the collocation method to a class of nonlinear singular integral equations with a Carleman shift preserving orientation on simple closed smooth Jordan curve in the generalized Holder space
In this paper, unsteady two-dimensional convective heat and mass transfer flow of a viscous, incompressible, electrically conducting optically thin fluid which is bounded by a vertical infinite plane surface was considered. A uniform applied homogeneous magnetic field is considered in the transverse direction with first order chemical reaction. An analytical solution for two-dimensional oscillatory flow on unsteady mixed convection of an incompressible viscous fluid, through a porous medium bounded by an infinite vertical plate in the presence of chemical reaction and thermal radiation are presented. The surface absorbs the fluid with a constant suction and the free stream velocity oscillates about a constant mean value. The resulting nonlinear partial differential equations were transformed into a set of ordinary differential equations using two-term series. The closed form solutions for velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number have been obtained, using the regular perturbation technique. Numerical evaluation of the analytical solutions was performed and the results are presented in tabular and graphical form. This illustrates the influence of the various parameters involved in the problem on the solutions.
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