11,171 research outputs found
Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems
A fast numerical technique for the solution of partial differential equations describing timedependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques. The effectiveness of the proposed technique is demonstrated by illustrative examples
New integral transform: Shehu transform a generalization of Sumudu and Laplace transform for solving differential equations
In this paper, we introduce a Laplace-type integral transform called the
Shehu transform which is a generalization of the Laplace and the Sumudu
integral transforms for solving differential equations in the time domain. The
proposed integral transform is successfully derived from the classical Fourier
integral transform and is applied to both ordinary and partial differential
equations to show its simplicity, efficiency, and the high accuracy
Joint densities of first hitting times of a diffusion process through two time dependent boundaries
Consider a one dimensional diffusion process on the diffusion interval
originated in . Let and be two continuous functions of
, with bounded derivatives and with and , . We study the joint distribution of the two random
variables and , first hitting times of the diffusion process through
the two boundaries and , respectively. We express the joint
distribution of in terms of and
and we determine a system of integral equations verified by
these last probabilities. We propose a numerical algorithm to solve this system
and we prove its convergence properties. Examples and modeling motivation for
this study are also discussed
Formalization of Transform Methods using HOL Light
Transform methods, like Laplace and Fourier, are frequently used for
analyzing the dynamical behaviour of engineering and physical systems, based on
their transfer function, and frequency response or the solutions of their
corresponding differential equations. In this paper, we present an ongoing
project, which focuses on the higher-order logic formalization of transform
methods using HOL Light theorem prover. In particular, we present the
motivation of the formalization, which is followed by the related work. Next,
we present the task completed so far while highlighting some of the challenges
faced during the formalization. Finally, we present a roadmap to achieve our
objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201
A new fractional derivative involving the normalized sinc function without singular kernel
In this paper, a new fractional derivative involving the normalized sinc
function without singular kernel is proposed. The Laplace transform is used to
find the analytical solution of the anomalous heat-diffusion problems. The
comparative results between classical and fractional-order operators are
presented. The results are significant in the analysis of one-dimensional
anomalous heat-transfer problems.Comment: Keywords: Fractional derivative, anomalous heat diffusion, integral
transform, analytical solutio
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