Showing papers on "Auxiliary function published in 1994"

A Set of Algorithms for the Incomplete Gamma Functions

Abstract: This paper gives fast and reliable algorithms for the numerical evaluation of the incomplete gamma functions and for auxiliary functions, such as functions related with the gamma function and error function. All these functions are of basic importance in applied probability problems.

Quantitative error estimates for coefficient idealization in linear elliptic problems

Abstract: We give a thorough quantitative error analysis for the effect of coefficient idealization on solutions of linear elliptic boundary value problems. The a posteriori error estimate is derived by a tactful application of the duality theory in convex analysis. The estimate involves an auxiliary function subject to certain constraint. We discuss in detail the selection of a good auxiliary function for various cases. Numerical examples show the effectiveness of our a posteriori error estimate.

Equi and uniform stability

Abstract: The subject of Liapunov functions constitutes a central theme in the theory of differential equations. It provides powerful tools that can be used to study the behavior of the solutions. The classical theorem of Liapunov on stability of the zero solutions for a given differential equation makes use of an auxiliary function which has to be positive definite. Also, the time derivative of this function, as computed along the solution, has to be negative definite. This auxiliary function is called a Liapunov function in the theory of differential equations or more generally dynamical systems theory.