In this paper, a new method is proposed in order to evaluate the stochastic solution of linear random differential equation. The method is based on the combination of the probabilistic transformation method for a single random variable and the numerical methods (e.g. finite difference, finite element, Runge-Kutta, etc...). The transformation technique evaluates the probability density function ...

The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity i...

The initial value problem for arbitrary order linear ordinary differential equations with constant coefficients is considered. The right-hand side of the equation and the initial conditions are affected by noise. Moreover, the values of the right-hand side are given only on a sparse set of discrete points. This type of problem arises in applications when the right-hand side or the initial condi...

Many important problems in the processing of Magnetic Resonance data can be reduced to well known ill-posed inverse problems. MR relaxometry, spectroscopy and MR image formation problems can be formulated respectively as the numerical inversion of Laplace transform, the modal analysis problem and the truncated trigonometric moment problem. A unified framework to efficiently solve these problems...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

Recently Sarathy and Muralidhar (2009) provided the first attempt at illustrating the implementation of differential privacy for numerical data. In this paper, we attempt to provide further insights on the results that are observed when Laplace based noise addition is used to protect numerical data in order to satisfy differential privacy. Our results raise serious concerns regarding the viabil...

In the paper, a technique of the numerical inversion of multidimensional Laplace transforms (nD NILT), based on a complex Fourier series approximation is elaborated in light of a possible ralative error achievable. The detailed error analysis shows a relationship between the numerical integration of a multifold Bromwich integral and a complex Fourier series approximation, and leads to a novel f...