Exact solution of a problem in a stellar atmosphere using the Laplace transform and the Wiener-Hopf technique

1979 ◽  
Vol 63 (1) ◽  
pp. 155-170 ◽  
Author(s):  
Rabindra Nath Das
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Stellar Atmosphere ◽  
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.

scholarly journals Rigorous time domain responses of polarizable media II

1998 ◽  
Vol 41 (3) ◽  
Author(s):  
M. Caputo ◽  
W. Plastino
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Time Domain ◽  
Input Data ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Discharge Data ◽  
Time Domain Data ◽  
Previous Note ◽  
The Laplace Transform

We present and test in detail with synthetic data a method which may be used to retrieve the parameters describing the induced polarization properties of media which fit the generally accepted frequency dependent formula of Cole and Cole (1941) (CC model). We use time domain data and rigorous formulae obtained from the exact solution of the problem found in a previous note (Caputo, 1996). The observed data considered here are the theoretical responses of the medium to box inputs of given duration in media defined with different parameters; however, as is usually done, only the discharge data are used (Patella >F2<et al.>F1<, 1987). The curve at the beginning of the discharge is studied in some detail. The method is successful in identifying the parameters when the data fit the CC model; if the medium is not exactly of the CC type the method may also help identify how the medium departs from the CC model. The Laplace Transform of the discharge for a box type input data is also given.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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