Abstract: A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.

finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

Abstract. This paper presents new formulations of the boundary-domain integral equation (BDIE) and the boundary-domain integro-differential equation (BDIDE) methods for the numerical solution of the two-dimensional Helmholtz equation with variable coefficients. When the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equa...

Reports and Memoranda No. 3447* August, z964 Summary. Existing methods of calculating the incompressible turbulent boundary layer have been critically examined and the results that they give compared with a large amount of published experimental data. The investigation has shown that different methods of calculating shape-factor development give, in general, widely different results and are in ...

In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed me...

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the timeand space-fractional diffusion equation with the quotient of the orders of the timeand space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then ...

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solito...