On the Computation of Rigorous Bounds for the Solutions of Linear Integral Equations With the Aid of Interval Arithmetic

A method is given for approximately solving linear Fredholm integral equations of the second klnd with non-negative kernels. The basis of the method is the construction of piecewise-polynomial degenerate kernels which bound the given kernel. The method is a generalization of a method suggested by Gerberich. When implemented on a computer, interval arithmetic is used so that rigorous bounds for the solution of the integral equations are obtained. The method is applied to two problems: the equation considered by Gerberich; and the equation of Love which arises in connection with the problem of determining the capacity of a circular plate condenser

Numerical methods for free and moving boundary problems

SIGLETIB Hannover: RO 7057(1986,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

NAXPERT. A prototype expert system for numerical software

SIGLETIB Hannover: RO 7057(1987,5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

An Irregular Grid Method for Solving High-Dimensional Problems In Finance

We propose and test a new method for pricing American options in a high dimensional setting. The method is centred around the approximation of the associated variational inequality on an irregular grid. We approximate the partial differential operator on this grid by appealing to the SDE representation of the stock process and computing the logarithm of the transition probability matrix of an approximating Markov chain. The results of numerical tests in five dimensions are promising