A singularly perturbed boundary value problem for a second-order equation in the case of variation of stability

1998 ◽  
Vol 63 (3) ◽  
pp. 311-318 ◽  
Author(s):  
V. F. Butuzov ◽  
N. N. Nefedov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Order Equation ◽  
Second Order ◽  
Singularly Perturbed

scholarly journals Numerical Solotion of a Problem of Fluid Filtration in a Viscoelastic Porous Medium

2020 ◽  
pp. 72-76
Author(s):  
R.A. Virts ◽  
A.A. Papin ◽  
W.A. Weigant
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Order Equation ◽  
Second Order ◽  
Initial System ◽  
Effective Pressure ◽  
Initial Boundary Value

The paper considers a model for filtering a viscous incompressible fluid in a deformable porous medium. The filtration process can be described by a system consisting of mass conservation equations for liquid and solid phases, Darcy's law, rheological relation for a porous medium, and the law of conservation of balance of forces. This paper assumes that the poroelastic medium has both viscous and elastic properties. In the one-dimensional case, the transition to Lagrange variables allows us to reduce the initial system of governing equations to a system of two equations for effective pressure and porosity, respectively. The aim of the work is a numerical study of the emerging initial-boundary value problem. Paragraph 1 gives the statement of the problem and a brief review of the literature on works close to this topic. In paragraph 2, the initial system of equations is transformed, as a result of which a second-order equation for effective pressure and the first-order equation for porosity arise. Paragraph 3 proposes an algorithm to solve the initial-boundary value problem numerically. A difference scheme for the heat equation with the righthand side and a Runge–Kutta second-order approximation scheme are used for numerical implementation.

ON A SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR A SECOND-ORDER DIFFERENTIAL EQUATION

2021 ◽  
Vol 1 (1) ◽  
pp. 33-41
Author(s):  
Keldibay Alymkulov ◽  
Kudaiberdi Gaparalievich Kozhobekov ◽  
Bektur Abdyrahmanovich Azimov ◽  
Nasipa Zulpukarovna Sultanova
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Singularly Perturbed ◽  
Second Order Differential Equation
Sign in / Sign up

Export Citation Format

Share Document