Exact solution of the problem of diffuse reflection and transmission in Rayleigh scattering by use of the Laplace transform and the theory of linear singular operators

1979 ◽  
Vol 60 (1) ◽  
pp. 221-232 ◽  
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Rayleigh Scattering ◽  
Diffuse Reflection ◽  
Reflection And Transmission ◽  
Singular Operators ◽  
The Laplace Transform

scholarly journals Laplace-SBA Method for Solving Nonlinear Coupled Burger's Equations

2021 ◽  
Vol 14 (3) ◽  
pp. 842-862
Author(s):  
Joseph Bonazebi-Yindoula
Keyword(s):  
Fluid Dynamics ◽  
Exact Solution ◽  
Numerical Methods ◽  
Laplace Transform ◽  
Exact Solutions ◽  
Partial Derivative ◽  
Basic Principles ◽  
The Laplace Transform ◽  
Fluid Dynamics Equations ◽  
Burger's Equations

Burger’s equations, an extension of fluid dynamics equations, are typically solved by several numerical methods. In this article, the laplace-Somé Blaise Abbo method is used to solve nonlinear Burger equations. This method is based on the combination of the laplace transform and the SBA method. After reminders of the laplace transform, the basic principles of the SBA method are described. The process of calculating the Laplace-SBA algorithm for determining the exact solution of a linear or nonlinear partial derivative equation is shown. Thus, three examplesof PDE are solved by this method, which all lead to exact solutions. Our results suggest that this method can be extended to other more complex PDEs.

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