Numerical-Analytical Method for Solving of the First Order Partial Quasi-Linear EquationsFikret A. Aliev, N.A. Aliev, K.G. Hasanov, A.P. Guliev, A.K. Turarov, G.V. Isaeva (pp. 158-164)
Abstract.Two-dimensional first order non-linear (quasi-linear) partial differential equation which arises in the solving of the system of hyperbolic equations describing of oil production by gas lift using the sweep method, is considered. By using the method of characteristics is shown that the seeking solution can be defined from the corresponding implicit algebraic relation by the help of the fixed point method. The computational algorithm for solving of implicit algebraic relation is giving. For the particular case , when the initial function is constant the analytical solution of the partial quasi linear equation is found.
Keywords:partial differential equation, quasi linear equation, method of characteristics, implicit solution, numerical algorithms, gas lift.