Time marching multilevel techniques for evolutionary dissipative problems (Q2719267)

A method for solving the nonlinear periodic Burgers problem is established. The problem is solved by means of a decomposition of the solution \(u\) in high \(z\) and low \(y\) modes components. For numerical analysis the linear equation is considered. The \(y\) and \(z\) components are determined by modified Runge-Kutta RK2 and RK4 nonconsistent implicit methods (NCIC) with a time step restriction according to the stability condition or to unconditional stability. Also consistent implicit modifications of the Euler and Runge-Kutta methods for solving this problem are indicated.NEWLINENEWLINENEWLINENumerical experiments are presented in comparison of NCIC, CIC4 and standard spectral method of collocation (SCM4) for the linear Burgers problem. For the nonlinear equation a comparison is carried out on numerical results obtained by NCIC1, CIC1 and SCM1 methods.