In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5075336 | PMC |
| http://dx.doi.org/10.1186/s40064-016-3487-4 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Transformation-Invariant Laplacian Metadevices Robust to Environmental Variation.
Adv Mater
January 2025
National Key Laboratory of Microwave Photonics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China.
As one of the typical applications of metamaterials, the invisibility cloak has raised vast research interests. After many years' research efforts, the invisibility cloak has extended its applicability from optics and acoustics to electrostatics and thermal diffusion. One scientific challenge that has significantly restricted the practical application of the invisibility cloak is the strong background dependence, that is, all passive cloaking devices realized thus far are unable to resist variation in the background refractive index.
View Article and Find Full Text PDFTheoretical and experimental study on the consolidation of soil with continuous drainage boundary under electroosmosis-surcharge preloading.
Sci Rep
December 2024
School of Civil Engineering, Shangqiu Lnstitute of Technology, Shangqiu, 476000, China.
Electroosmosis and surcharge preloading represent two effective soil consolidation methodologies. Their combined application has been proven to be effective in shortening the consolidation period and mitigating the degradation of electroosmotic consolidation performance due to crack generation. In this study, an axisymmetric free-strain consolidation analytical model incorporating a continuous drainage top boundary was established.
View Article and Find Full Text PDFModeling and analysis of dengue transmission in fuzzy-fractional framework: a hybrid residual power series approach.
Sci Rep
December 2024
Department of Mathematics, Ghazni University, Ghazni, Afghanistan.
The current manuscript presents a mathematical model of dengue fever transmission with an asymptomatic compartment to capture infection dynamics in the presence of uncertainty. The model is fuzzified using triangular fuzzy numbers (TFNs) approach. The obtained fuzzy-fractional dengue model is then solved and analyzed through fuzzy extension of modified residual power series algorithm, which utilizes residual power series along with Laplace transform.
View Article and Find Full Text PDFA signal processing tool adapted to the periodic biphasic phenomena: the Dynalet transform.
Math Med Biol
December 2024
Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, General Cruz 222, Valparaíso, Chile.
The linear functional analysis, historically founded by Fourier and Legendre (Fourier's supervisor), has provided an original vision of the mathematical transformations between functional vector spaces. Fourier, and later Laplace and Wavelet transforms, respectively defined using the simple and damped pendulum, have been successfully applied in numerous applications in Physics and engineering problems. However the classical pendulum basis may not be the most appropriate in several problems, such as biological ones, where the modelling approach is not linked to the pendulum.
View Article and Find Full Text PDFChaotic property in general fractional calculus.
Chaos
December 2024
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, Kiev 01024, Ukraine.
We prove the chaos property, in the sense of Devaney, of the discrete-time fractional derivative understood in the framework of general fractional calculus. The latter means the discretization of a differential-convolution operator whose kernel has the Laplace transform belonging to the Stieltjes class.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!