COMPARISON OF NUMERICAL ALGORITHMS FOR ON E-DIMENSIONAL NONLINEAR VORTICITY EQUATION SOLUTION

Numerical aspects of the solution of the initial-boundary value proble m for one-dimensional nonlinear vorticity equation is under considerat ion. A theorem of existence and uniqueness of the solution of differen tial problem is formulated. The computational experiments are carried out using two different numerical techniques: finite element leap-frog scheme and finite difference implicit splitting-up method. The charac teristics of these two methods under different input parameters includ ing nonlinearity shear and viscosity coefficients are compared. In the ''weakly'' nonlinear case, both methods obtain similar results in the sense of precision. In the ''moderate'' nonlinear case, the methods h ave different results. The 1-st method (leap-frog) is not able to comp ute with small viscosity coefficient but for large one this scheme all ows a large time step. The 2-nd method (splitting) allows to use very small viscosity coefficients. The error of approximation for the 2-nd method is greater but it converges faster than the 1-st.