The aim of this study is to give a Legendre polynomial approximation for the solution of the second order linear hyper-bolic partial differential equations (HPDEs) with two variables and constant ...

This project focuses on solving Bessel's and Legendre's differential equations using Physics-Informed Neural Networks (PINN). By integrating domain knowledge directly into the neural network, we ...

This equation provides the raw solution to the Legendre differential equation without any additional normalization. It is useful for understanding the basic structure of the Legendre polynomials. The ...

1 Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, KSA 2 Department of Mathematics, Faculty of Science, Benha University, ...

Abstract: Based on analyzing the properties of Legendre wavelets, the extended Legendre wavelets, defined on interval (-r, r), is achieved and its properties are considered. According to the ...

Abstract: This paper presents an overview of several integral equation (IE) formulations where the use of Legendre basis functions is beneficial. Specifically, we introduce the basis functions and ...

A note on the generalized and universal associated Legendre equations Citation: Kirk, K. L. A. , Bryenton, K. R. , & Saad, N. . (2018). A note on the generalized and universal associated Legendre ...

SIAM Journal on Numerical Analysis, Vol. 33, No. 4 (Aug., 1996), pp. 1534-1558 (25 pages) We are interested in the study of a fast algorithm introduced by Brenier computing the discrete ...

We tested different optical elements placed in three different positions by applying the irradiance transport equation (ITE), obtaining the wavefront $[ W(x,y) ]$[W(x ...

Analytical models of axially symmetric thin disks of finite extension in the presence of magnetic field are presented based on the well-known Morgan–Morgan solutions. The source of the magnetic field ...