Numerical stability in dynamic elastic-plastic problems
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
We study the problem of interpolation by a complete spline of 2n − 1 degree given in B-spline representation. Explicit formulas for the first nand the last ncoefficients of B-spline decomposition are found. It is shown that other B-spline coefficients can be computed as a solution of a banded system of an equitype linear equations.
We present a local and a semi-local convergence analysis of an iterative method for approximating zeros of derivatives for solving univariate and unconstrained optimization problems. In the local case, the radius of convergence is obtained, whereas in the semi-local case, sufficient convergence criteria are presented. Numerical examples are also provided.