Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness

This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method. The recovery of the solution of the original random partial differential problem throughout the inverse integral transform allows its numerical approximation using Gaussian quadratures involving the evaluation of the solution of the random ordinary differential problem at certain concrete values, which are approximated using Monte Carlo method. Numerical experiments illustrating the numerical convergence of the method are included.

RESEARCH OF TEMPERATURE PROFILES IN THE WELL IN THE COURSE OF PUMPING LIQUID ON THE BASIS OF NUMERICAL INVERSION OF ISEGER

The analysis of a temperature profile in the trunk of a vertical well when pumping liquid was carried out. The paper describes the application of an algorithm of the inverse numerical transformation with use of Gaussian quadratures (Iseger's method) to a task about a temperature profile under conditions of a short-term liquid pumping into the well. Analytical dependences are constructed on the basis of a method of the Laplace-Carson integral transformation of decomposition. The inverse transition is carried out on the basis of numerical inversion with use of Gaussian quadratures (Iseger's method).

Generalized Gaussian quadratures for integrals with logarithmic singularity

A short account on Gaussian quadrature rules for integrals with logarithmic singularity, as well as some new results for weighted Gaussian quadrature formulas with respect to generalized Gegenbauer weight x |? |x|(1-x2)?, ? > -1, on (-1,1), which are appropriated for functions with and without logarithmic singularities, are considered. Methods for constructing such kind of quadrature formulas and some numerical examples are included.