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Spectral Method for the Heat Equation with Axial Symmetry and a Source
In this paper, we present a spectral method for solving the heat equation in cylindrical coordinates in a case where the data are axisymmetric and independent of the z-coordinate at the same time. The spectral method considered is of GalerkintypewithaGauss-Radaunumericalquadratureformula, itisbasedonaweightedweakvariationalformulationofthe ...
New search direction of steepest descent method for solving large linear systems
The steepest descent (SD) method is well-known as the simplest method in optimization. In this paper, we propose a new SD search direction for solving system of linear equations Ax = b. We also prove that the proposed SD method with exact line search satisfies descent condition and possesses global ...