Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation

In this paper, we propose an efficient numerical method for solving initial boundary value problem a coupled system of equations consisting nonlinear parabolic partial integro-differential equation and elliptic with term. This has important applied significance in petroleum engineering finds application modeling two-phase nonequilibrium fluid flows porous medium generalized law. The construction the is based on employing finite element spatial direction difference approximation to time derivative. Newton’s second-order formula are treatment terms. stability convergence discrete scheme as well iterative process rigorously proven. Numerical tests conducted confirm theoretical analysis. constructed study flow incompressible medium. addition, present two examples models allowing prediction behavior that reduced studied paper.