Parallel Number Theoretical Numerics for Solving s-dimensional Integral Equations of the Convolution Type

Abstract

This paper is devoted to show that parallel number theoretical methods for solving special types of the integral equation \Phi(T ) = F (T ) + (K \Phi)(T ) 2 IR for higher dimensions s can be very efficient with a view to accuracy and computation time. To enable a numerical solution of such integral equations we will follow a classical way which will lead us to the problem of the inversion of multivariate Laplace transforms. The inherent parallelism of the number theoretical methods to compute the inversion of the s-dimensional Laplace transform has been exploited