TIME-STEP METHOD OF LAPLACE TRANSFORMATION NUMERICAL INVERSION BASED ON THE RUNGE - KUTTA SCHEME NODES WITH A VARIABLE STEP OF INTEGRATION

Abstract

The paper is dedicated to the development of time-step method for numerical inversion of Laplace transformation, based on the original function integration theorem. Derived stepping scheme is determined by the choice of quadrature formula with a key and the choice of numerical solution scheme for Cauchy problem, which arises for the Volterra integral. Quadrature formula with a key is a result of special highly oscillatory integration. The approach is used to numerically obtain displacement & pore pressure originals for a one-dimensional poroelastic problem.

Keywords: Laplace transformation inversion, time-step method, Runge − Kutta scheme, highly oscillatory quadrature, one-dimensional poroelastic problem.