Search · four archives
Search · four archives
21 papers · ranked by Valyu relevance
Omer Acan, Yıldıray Keskin
In this study, approximate solution of Kuramoto–Sivashinsky Equation, by the reduced differential transform method, are presented. We apply this method to an example. Thus, we have obtained numerical solution Kuramoto– Sivashinsky equation. Comparisons are made between the exact solution and the reduced differential…
Jamshad Ahmad, Syed Tauseef Mohyud-Din, Enrique Hernandez-Lemus
In this paper, a fractional complex transform (FCT) is used to convert the given fractional partial differential equations (FPDEs) into corresponding partial differential equations (PDEs) and subsequently Reduced Differential Transform Method (RDTM) is applied on the transformed system of linear and nonlinear…
Murat Gubes
Reduced Differental Transform Method (RDTM) which is one of the useful and effective numerical approximate method is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE). Also, we compared the presented method with the famous Adomian Decomposition and Laplace Decomposition Technique. So, the results…
Murat Gubes
This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering, biological and etc. models as an alternative to obtain reliable and fastest…
Eman Abuteen, Asad Freihat, Mohammed Al‐Smadi, Hammad Khalil + 1 more
'Rahmat Ali Khan'] Abstract: This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides…
Salah Abuasad, Ahmet Yildirim, Ishak Hashim, Samsul Ariffin Abdul Karim + 1 more
'Samsul Ariffin Abdul Karim' 'J.F. Gómez-Aguilar'] In this paper, we applied a fractional multi-step differential transformed method, which is a generalization of the multi-step differential transformed method, to find approximate solutions to one of the most important epidemiology and mathematical ecology, fractional…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Fernando Henríquez, Jan S. Hesthaven
Reduction and the Laplace Transform Authors: ['Fernando Henríquez' 'Jan S. Hesthaven'] Abstract. We introduce a novel, fast method for the numerical approximation of parabolic partial differential equations (PDEs for short) based on model order reduction techniques and the Laplace transform. We start by applying said…
Heather A. Harrington, Robert A. Van Gorder
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where…
Ricardo Reyes
In this paper, we propose the Frequency Reduced-Basis method: a reduced-basis method to solve time-dependent partial differential equations based on the Laplace transform. Unlike traditional approaches, we begin by applying the Laplace transform to the evolution problem, yielding a timeindependent boundary value…
Fernando López-Caamal, Tatiana T. Marquez-Lago, Lars Kaderali
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is…
Pablo Hernández-Becerro, Daniel Spescha, Konrad Wegener
Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction…
Meghan O’Connell, Misha E. Kilmer, Eric de Sturler, Serkan Gugercin
In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of the optimization process. In the context of absorption imaging in diffuse…
Jonathan M. Taylor
Light field microscopy can capture 3D volume datasets in a snapshot, making it a valuable tool for high-speed 3D imaging of dynamic biological events. However, subsequent computational reconstruction of the raw data into a human-interpretable 3D+time image is very time-consuming, limiting the technique’s utility as a…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Eric Rawls
Time-frequency (TF) analysis of M/EEG data enables rich understanding of cortical dynamics underlying cognition, health, and disease. There are many algorithms for time-frequency decomposition of M/EEG neural data, but they are implemented in an inconsistent manner and most existing toolboxes either 1) contain only one…
Ruonan Shi, Jae-Hun Jung, Ferdinand Schweser
The MRI image is obtained in the spatial domain from the given Fourier coefficients in the frequency domain. It is costly to obtain the high resolution image because it requires higher frequency Fourier data while the lower frequency Fourier data is less costly and effective if the image is smooth. However, the Gibbs…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Alexandru V. Avram, Kadharbatcha S. Saleem, Peter J. Basser
Diffusion MRI studies with resolutions of a few hundred micrometers have consistently shown that in the cortex water diffusion occurs preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if…
Authors not listed
Electrochemical impedance spectroscopy (EIS) is a powerful analytical technique for studying electrochemical systems, offering broad frequency range coverage and straightforward implementation. However, EIS measurements at low frequencies are limited by both lengthy acquisition times and the risk of disrupting…