Modeling of hydrodynamic processes in oil reservoirs is an urgent task in the oil production industry. With the help of models, it is possible to predict the behavior of the reservoir in real conditions. Newton's method is the basis of many algorithms used to solve modeling problems. In this paper, a model of the motion of a two-phase fluid is considered. The equations describing fluid motion are a nonlinear system that is linearized by Newton's method. The resulting system of linear equations is solved by the method of generalized minimal residuals. To speed up the calculation time, the algorithm of the method of generalized minimal residuals with restarts is used. The developed algorithms were tested and the results were analyzed. Numerical results have shown that for the problem of pumping water into an oil reservoir, the algorithm of the generalized minimal residual method with restarts works faster than the algorithm without modifications, but requires practical determination of the optimal value of iteration steps for restart.