scholarly journals Mean square solution of Bessel differential equation with uncertainties

2017 ◽  
Vol 309 ◽  
pp. 383-395 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
L. Villafuerte
Keyword(s):  
Differential Equation ◽  
Mean Square ◽  
Bessel Differential Equation ◽  
Mean Square Solution

scholarly journals Calculating Galois groups of third-order linear differential equations with parameters

2018 ◽  
Vol 20 (04) ◽  
pp. 1750038
Author(s):  
Andrei Minchenko ◽  
Alexey Ovchinnikov
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Galois Group ◽  
Galois Groups ◽  
Linear Differential Equations ◽  
Unipotent Radical ◽  
Third Order ◽  
Differential Galois Group ◽  
Bessel Differential Equation ◽  
Linear Differential

Motivated by developing algorithms that decide hypertranscendence of solutions of extensions of the Bessel differential equation, algorithms computing the unipotent radical of a parameterized differential Galois group have been recently developed. Extensions of Bessel’s equation, such as the Lommel equation, can be viewed as homogeneous parameterized linear differential equations of the third order. In this paper, we give the first known algorithm that calculates the differential Galois group of a third-order parameterized linear differential equation.

Solution to the Bessel differential equation with interactive fuzzy boundary conditions

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
Daniel Eduardo Sánchez ◽  
Vinícius Francisco Wasques ◽  
Estevão Esmi ◽  
Laécio Carvalho de Barros
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Bessel Differential Equation ◽  
Fuzzy Boundary

scholarly journals Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020 ◽  
Vol 52 (3) ◽  
pp. 735-771
Author(s):  
Christel Geiss ◽  
Céline Labart ◽  
Antti Luoto
Keyword(s):  
Differential Equation ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Backward Stochastic Differential Equation ◽  
Stochastic Equations ◽  
Terminal Condition ◽  
Probabilistic Methods ◽  
Mean Square ◽  
Finite Difference Equations ◽  
Backward Sdes

AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.

scholarly journals Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric

2015 ◽  
Vol 18 (2) ◽  
pp. 14-20
Author(s):  
Dung Anh Tran ◽  
Hang Thi Chu ◽  
Long Ta Bui
Keyword(s):  
Differential Equation ◽  
Bessel Function ◽  
Bessel Functions ◽  
Analytic Solutions ◽  
Air Pollutant ◽  
Spherical Coordinates ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Bessel Differential Equation ◽  
Separation Of Variable

The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation.

Sign in / Sign up

Export Citation Format

Share Document