The second-order upwind finite difference fractional steps method for moving boundary value problem of oil-water percolation

2014 ◽  
Vol 30 (4) ◽  
pp. 1103-1129 ◽  
Author(s):  
Yuan Yirang ◽  
Li Changfeng ◽  
Sun Tongjun
Keyword(s):  
Finite Difference ◽  
Boundary Value Problem ◽  
Moving Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Water Percolation ◽  
Oil Water ◽  
Upwind Finite Difference

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

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