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On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse laplace transform Methods

Computer Modeling in Engineering & Sciences 2023年第6期135卷 2743-2765页

作者： Kamran Siraj Ahmad Kamal Shah Thabet Abdeljawad Bahaaeldin Abdalla Department of Mathematics Islamia College PeshawarKhyber Pakhtoon KhwaPeshawar25120Pakistan Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan

laplace transform is one of the powerful tools for solving differential equations in engineering and other science *** the laplace transform for solving differential equations,however,sometimes leads to solutions in the laplace domain that are not readily invertible to the real domain by ***,we need numerical inversionmethods to convert the obtained solution fromlaplace domain to a real *** this paper,we propose a numerical scheme based on laplace transform and numerical inverse laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main ***,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo ***,we transformthe fractional differential equation in Caputo sense to an equivalent equation in laplace *** the solution of the transformed equation is obtained in laplace ***,the solution is converted into the real domain using numerical inversion of laplace *** inversion methods are evaluated in this paper,and their convergence is also *** test problems are used to validate the inversion *** demonstrate our results with the help of tables and *** obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

关键词： Fractal-fractional differential equation power law kernel exponential decay kernel Mittag-Leffler kernel laplace transform Euler’s method Talbot’s method Stehfest’s method

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Numerical inversion method for the laplace transform based on Boubaker polynomials operational matrix

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第1期13卷 251-264页

作者： Rachid Belgacem Ahmed Bokhari Salih Djilali Sunil Kumar Faculty of Exact and Computer Sciences Mathematic Department Hassiba Benbouali UniversityChlefAlgeria Laboratory of Mathematics and its Applications(LMA)Faculty of Exact and Computer Sciences Hassiba Benbouali University ChlefAlgeria Laboratoire d’Analyse Non Lineaire et Mathematiques Appliquees Universite de Tlemcen TlemcenAlgeria Department of Mathematics National Institute of Technology Jamshedpur 831014JharkhandIndia

We investigate through this research the numerical inversion technique for the laplace transforms cooperated by the integration Boubaker polynomials operational *** efficiency of the presented approach is demonstrated by solving some differential ***,this technique is combined with the standard laplace Homotopy Per-turbation *** numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

关键词： laplace transform Boubaker polynomials operational matrix homotopy per-turbation method numerical method

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Contrast Enhancement Using Weighted Coupled Histogram Equalization with laplace transform

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Journal of Harbin Institute of Technology(New Series) 2022年第4期29卷 32-40页

作者： Huimin Hao Wenbin Xin Minglong Bu He Wang Yuan Lan Xiaoyan Xiong Jiahai Huang College of Mechanical and Vehicle Engineering Taiyuan University of TechnologyTaiyuan 030024China Harbin Electric Machinery Company Limited Harbin 150040China

Histogram equalization is a traditional algorithm improving the image contrast,but it comes at the cost of mean brightness shift and details *** order to solve these problems,a novel approach to processing foreground pixels and background pixels independently is proposed and *** details are mainly contained in the foreground,the weighted coupling of histogram equalization and laplace transform were adopted to balance contrast enhancement and details *** weighting factors of image foreground and background were determined by the amount of their respective *** proposed method was conducted to images acquired from CVG⁃UGR and US⁃SIPI image databases and then compared with other methods such as clipping histogram spikes,histogram addition,and non⁃linear transformation to verify its *** show that the proposed algorithm can effectively enhance the contrast without introducing distortions,and preserve the mean brightness and details well at the same time.

关键词： contrast enhancement weighted processing histogram equalization laplace transform

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laplace transform OF THE SURVIVAL PROBABILITY UNDER SPARRE ANDERSEN MODEL

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Applied Mathematics(A Journal of Chinese Universities) 2007年第1期22卷 109-118页

作者： Sun Chuanguang Department of Mathematics Qufu Normal University Qufu 273165 China Department of Basic Science Shandong Water Polytechnic Rizhao 276826 China

In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.

关键词： Andersen model survival probability laplace transform Lundberg's fundamental equation.

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A Joint laplace transform for Pre-exit Diffusion of Occupation Times

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Acta Mathematica Sinica,English Series 2017年第4期33卷 509-525页

作者： Ye CHEN Xiang Qun YANG Ying Qiu LI Xiao Wen ZHOU College of Mathematics and Computer Science Hu'nan Normal University College of Mathematics and Computational Science Hu’nan University of Arts and Science College of Mathematics and Statistics Changsha University of Science and Technology Department of Mathematics and Statistics Concordia University

For a < r < b, the approach of Li and Zhou(2014) is adopted to find joint laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from eithe... 详细信息

For a laplace transforms of occupation times over intervals(a, r) and(r, b) for a time homogeneous diffusion process before it first exits from either a or b. The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions on the joint laplace transforms of occupation times for Brownian motion with drift, Brownian motion with alternating drift and skew Brownian motion, respectively.

关键词： laplace transform occupation time time-homogeneous diffusion exit time Brownian motion with alternating drift skew Brownian motion

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THE EXTENDED JORDAN'S LEMMA AND THE RELATION BETWEEN laplace transform AND FOURIER transform

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Applied Mathematics and Mechanics(English Edition) 1997年第6期18卷 571-574页

作者：魏志勇诸永泰 Institute of Modern Physics Academia Sinica Lanzhou P. R. China

Jordan's lemma can be used for a wider range than the original one. The extended Jordan's lemma can be described as follows. Let f(z) be analytic in the upper half of the z plane (Imz≥0), with the exception of a finite number of isolated singularities, and for P>o, if then where z=Rei and CR is the open semicircle in the upper half of the z *** the extended Jordan's lemma one can find that laplace transform and Fourier transform are a pair of integral transforms which relate to each other.

关键词： extended Jordan's lemma laplace transform Fourier transform,complex variable function

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The Numerical Inversion of the laplace transform in a Multi-Precision Environment

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Applied Mathematics 2022年第5期13卷 401-418页

作者： Colin L. Defreitas Steve J. Kane School of Physics Astronomy and Mathematics University of Hertfordshire Hertfordshire UK

This paper examines the performance of five algorithms for numerically inverting the laplace transform, in standard, 16-digit and multi-precision environments. The algorithms are taken from three of the four main classes of numerical methods used to invert the laplace transform. Because the numerical inversion of the laplace transform is a perturbed problem, rounding errors which are generated in numerical approximations can adversely affect the accurate reconstruction of the inverse transform. This paper demonstrates that working in a multi-precision environment can substantially reduce these errors and the resulting perturbations exist in transforming the data from the s-space into the time domain and in so doing overcome the main drawback of numerically inverting the laplace transform. Our main finding is that both the Talbot and the accelerated Gaver functionals perform considerably better in a multi-precision environment increasing the advantages of using laplace transform methods over time-stepping procedures in solving diffusion and more generally parabolic partial differential equations.

关键词： laplace transform Perturbation Numerical Inversion Multi-Precision Stehfest Talbot

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Solution of the Schrodinger equation for a particular form of Morse potential using the laplace transform

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Chinese Physics C 2013年第4期37卷 36-38页

作者： M.Zarezadeh M.K.Tavassoly Atomic and Molecular Group Faculty of PhysicsYazd University Photonics Research Group Engineering Research CenterYazd University

In this paper, we have solved the Schrdinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the laplace transform technique wh... 详细信息

关键词： Schrdinger equation laplace transform Morse potential bound state

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A Hybrid Finite Element-laplace transform Method for the Analysis of Transient Electromagnetic Scattering by an Over-Filled Cavity in the Ground Plane

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Communications in Computational Physics 2009年第1期5卷 126-141页

作者： Junqi Huang Aihua W.Wood Michael J.Havrilla Air Force Institute of Technology 2950 Hobson WayWright-Patterson AFBOH 45433USA

A hybrid finite element-laplace transform method is implemented to analyze the time domain electromagnetic scattering induced by a 2-D overfilled cavity embedded in the infinite ground *** algorithm divides the whole scattering domain into two,interior and exterior,*** the interior sub-domain which covers the cavity,the problem is solved via the finite element *** problem is solved analytically in the exterior sub-domain which slightly overlaps the interior subdomain and extends to the rest of the upper half *** use of the laplace transform leads to an analytical link condition between the overlapping *** analytical link guides the selection of the overlapping zone and eliminates the need to use the conventional Schwartz *** dramatically improves the efficiency for solving transient scattering *** solutions are tested favorably against analytical ones for a canonical *** perfect link over the artificial boundary between the finite element approximation in the interior and analytical solution in the exterior further indicates the reliability of the *** error analysis is also performed.

关键词： Overfilled cavity time domain electromagnetic scattering laplace transform finite element method

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APPLICATIONS OF HAMILTONIAN AND laplace transform IN AN ECONOMIC MODEL

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Acta Mathematica Scientia 2000年第4期20卷 442-450页

作者：龚六堂 Guanghua School of Management Peking University Beijing 100871 China Institute of Advanced Economic Studies Wuhan University Wuhan 430072 China

This paper analyzes the long-run effects and short-run effects of foreign aid on the domestic economy by using the Hamilton system and laplace transform. It is found that an increase in the foreign aid has no long-run effect on the foreigll borrowing, domestic capital accumulation and the foreign direct investment in the home country, but increases the steady-state consumption level the same amount. However, the short-run analysis presents that increasing foreign aid does not affect the initial consumptioll level and the initial consumption increase rate; but it affects the initial savings positively.

关键词： Hamilton system laplace transform foreign aid capital accumulation

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