On Solution of Boundary Layer Problems Conversed to System of First-Order Partial Differential Equations with Quadratic Nonlinearity

The system of boundary layer differential equations has been conversed to a system of first-order partial differential equations with quadratic nonlinearity which presents a generalized system of equations of Riccati type. After the representation of the required vector-function as asymptotic series, finding the boundary problem solution for this system is reduced to solving systems of second-order algebraic equations. The stationary two-dimensional boundary layer problem solution is obtained and its conformity with the known numerical solution is proved. The nonstationary two-dimensional problem of forming boundary layer in accelerated fluid motion is solved within the time interval from zero to infinity, where the solution of the nonstationary problem becomes that of the stationary one.