scholarly journals On an algorithm for the problem of tracking a trajectory of a parabolic equation

2017 ◽  
Vol 27 (3) ◽  
pp. 457-465 ◽  
Author(s):  
Marina Blizorukova ◽  
Vyacheslav Maksimov
Keyword(s):  
Parabolic Equation ◽  
Large Time ◽  
Time Interval ◽  
Stable Algorithm ◽  
Shift Method ◽  
Large Time Interval ◽  
Extremal Shift

AbstractIn this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.

One dimensional vertical infiltration

Soil Research ◽  
1972 ◽  
Vol 10 (2) ◽  
pp. 143 ◽  
Author(s):  
T Talsma ◽  
J Parlange
Keyword(s):  
Hydraulic Conductivity ◽  
Boundary Conditions ◽  
Soil Properties ◽  
Field Data ◽  
Large Time ◽  
Three Dimensional ◽  
Time Interval ◽  
Large Time Interval ◽  
One Dimensional ◽  
Field Soils

Various concise equations have been proposed, and used, to describe the dynamics of one-dimensional, vertical, infiltration into uniform soils. Such equations, even when initial and boundary conditions are satisfied, do not describe infiltration with equal accuracy for all materials, especially when applied over a large time interval. Recently proposed equations appear more reliable and require only two, easily measurable, soil properties, viz., sorptivity and hydraulic conductivity, for application in most practical situations. Numerical, laboratory, and field data are presented. These adequately support the reliability of the solutions. The applicability of the solutions to field soils with systematically varying conductivity is more restricted than the two- or three-dimensional solutions.

Sign in / Sign up

Export Citation Format

Share Document