Numerical solution of distributed order fractional differential equations by hybrid functions

S Mashayekhi, M Razzaghi - Journal of computational physics, 2016 - Elsevier
In this paper, a new numerical method for solving the distributed fractional differential
equations is presented. The method is based upon hybrid functions approximation. The …

A single layer fractional orthogonal neural network for solving various types of Lane–Emden equation

AH Hadian-Rasanan, D Rahmati, S Gorgin, K Parand - New Astronomy, 2020 - Elsevier
Lane–Emden equation is an important nonlinear singular second order differential equation
which can express various phenomena in astrophysics. On the other hand, by growing …

A new Taylor series based numerical method: Simple, reliable, and promising

JH He, L Verma, B Pandit, AK Verma… - Journal of Applied and …, 2023 - jacm.scu.ac.ir
Taylor series method is a simple analytical method, which is accessible to all non-
mathematician, has slow convergence. This paper develops a new Taylor series based …

GEPINN: An innovative hybrid method for a symbolic solution to the Lane-Emden type equation based on grammatical evolution and physics-informed neural …

HD Mazraeh, K Parand - Astronomy and Computing, 2024 - Elsevier
In this paper, we present an innovative and powerful combination of grammatical evolution
and a physics-informed neural network approach for symbolically solving the Lane-Emden …

Learning nonlinear dynamics with behavior ordinary/partial/system of the differential equations: looking through the lens of orthogonal neural networks

M Omidi, B Arab, AHH Rasanan, JA Rad… - Engineering with …, 2022 - Springer
Applications of neural network algorithms have been grown in recent years and various
architectures have been introduced by researchers for the purpose of solving different types …

Orthonormal Bernoulli wavelets neural network method and its application in astrophysics

P Rahimkhani, Y Ordokhani - Computational and Applied Mathematics, 2021 - Springer
The purpose of this paper is to present two efficient computational schemes for solving Lane–
Emden type equations based on an artificial neural network. The mentioned neural network …

[PDF][PDF] A numerical approach to solve Lane-Emden type equations by the fractional order of rational Bernoulli functions

K Parand, H Yousefi, M Delkhosh - Romanian J. Phys, 2017 - rjp.nipne.ro
In this paper, a numerical method based on the hybrid of the quasilinearization method
(QLM) and the collocation method is suggested for solving wellknown nonlinear Lane …

High-order shifted Gegenbauer integral pseudo-spectral method for solving differential equations of Lane–Emden type

KT Elgindy, HM Refat - Applied Numerical Mathematics, 2018 - Elsevier
We present a novel, high-order, efficient, and exponentially convergent shifted Gegenbauer
integral pseudo-spectral method (SGIPSM) to solve numerically Lane–Emden equations …

Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting

L Xu, M Aouad - Applied Mathematics and Nonlinear Sciences, 2021 - sciendo.com
In order to study the fair value analysis of financial accounting, the Euler wavelet method is
proposed to solve the numerical solutions of a class of Lane-Emden type differential …

A New Constructing Rational Functions Method For Solving Lane− Emden Type Equations

J He, Z Zheng, C Du - Neural Processing Letters, 2023 - Springer
In this paper, a new construction machine learning method is proposed based on Rational
Chebyshev polynomials to solve Lane–Emden type differential equations. The method is …