scholarly journals SPLINE DIFFERENCE SCHEME FOR TWO-PARAMETER SINGULARLY PERTURBED PARTIAL DIFFERENTIAL EQUATIONS

2014 ◽  
Vol 32 (1_2) ◽  
pp. 185-201 ◽  
Author(s):  
W.K. Zahra ◽  
M.S. El-Azab ◽  
Ashraf M. El Mhlawy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Singularly Perturbed ◽  
Partial Differential ◽  
Two Parameter

scholarly journals The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation

2021 ◽  
Vol 29 (2) ◽  
pp. 126-145
Author(s):  
Mohamed A. Bouatta ◽  
Sergey A. Vasilyev ◽  
Sergey I. Vinitsky
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Small Parameter ◽  
Asymptotic Method ◽  
Planck Equation ◽  
Singularly Perturbed ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Fokker Planck

The asymptotic method is a very attractive area of applied mathematics. There are many modern research directions which use a small parameter such as statistical mechanics, chemical reaction theory and so on. The application of the Fokker-Planck equation (FPE) with a small parameter is the most popular because this equation is the parabolic partial differential equations and the solutions of FPE give the probability density function. In this paper we investigate the singularly perturbed Cauchy problem for symmetric linear system of parabolic partial differential equations with a small parameter. We assume that this system is the Tikhonov non-homogeneous system with constant coefficients. The paper aims to consider this Cauchy problem, apply the asymptotic method and construct expansions of the solutions in the form of two-type decomposition. This decomposition has regular and border-layer parts. The main result of this paper is a justification of an asymptotic expansion for the solutions of this Cauchy problem. Our method can be applied in a wide variety of cases for singularly perturbed Cauchy problems of Fokker-Planck equations.

Impact on Partial Differential Equations Filtering Models of Difference Scheme

2015 ◽  
Vol 52 (9) ◽  
pp. 091004
Author(s):  
王琳霖 Wang Linlin ◽  
唐晨 Tang Chen ◽  
王亚杰 Wang Yajie
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Partial Differential
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