Analytic solution of boundary-value problems for nonstationary model kinetic equations

1992 ◽  
Vol 92 (1) ◽  
pp. 782-790 ◽  
Author(s):  
A. V. Latyshev ◽  
A. A. Yushkanov
Keyword(s):  
Boundary Value Problems ◽  
Analytic Solution ◽  
Boundary Value ◽  
Kinetic Equations ◽  
Model Kinetic Equations ◽  
Nonstationary Model

Contemporary Methods for the Numerical-Analytic Solution of Boundary-Value Problems in Noncanonical Domains

2020 ◽  
Vol 247 (1) ◽  
pp. 88-107
Author(s):  
P. Shakeri Mobarakeh ◽  
V. T. Grinchenko ◽  
V. V. Popov ◽  
B. Soltannia ◽  
G. M. Zrazhevsky
Keyword(s):  
Boundary Value Problems ◽  
Analytic Solution ◽  
Boundary Value

scholarly journals Galerkin Method for Nonlinear Higher-Order Boundary Value Problems Based on Chebyshev Polynomials

2021 ◽  
Vol 2128 (1) ◽  
pp. 012035
Author(s):  
W. Abbas ◽  
Mohamed Fathy ◽  
M. Mostafa ◽  
A. M. A Hesham
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Chebyshev Polynomials ◽  
Nonlinear Boundary ◽  
Analytic Solution ◽  
Boundary Value ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Algebraic Set ◽  
The Galerkin Method

Abstract In the current paper, we develop an algorithm to approximate the analytic solution for the nonlinear boundary value problems in higher-order based on the Galerkin method. Chebyshev polynomials are introduced as bases of the solution. Meanwhile, some theorems are deducted to simplify the nonlinear algebraic set resulted from applying the Galerkin method, while Newton’s method is used to solve the resulting nonlinear system. Numerous examples are presented to prove the usefulness and effectiveness of this algorithm in comparison with some other methods.

Kinetic Theory of Molecular Gases I: Models of the Linear Waldmann–Snider Collision Operator

1975 ◽  
Vol 53 (13) ◽  
pp. 1266-1278 ◽  
Author(s):  
G. Tenti ◽  
Rashmi C. Desai
Keyword(s):  
Kinetic Theory ◽  
Boundary Value Problems ◽  
Transport Properties ◽  
Boundary Value ◽  
Kinetic Equations ◽  
Collision Operator ◽  
Matrix Elements ◽  
Molecular Gases ◽  
The Matrix ◽  
Modeling Theory

Using a method closely akin to the Gross–Jackson–Sirovich procedure, we present a modeling theory of the linear Waldmann–Snider collision operator. The resulting model kinetic equations are applicable to all regions of wavelength and frequency consistent with the original equation itself. The theory is made parameter free by relating the matrix elements of the collision operator to measured transport properties. It is sophisticated enough to afford a study of both scalar and tensorial phenomena and can be applied to the analysis of a variety of initial and boundary value problems.

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