Numerical Solution of Resonantly Forced ODE with Applications to Weakly Nonlinear Instability of Shallow Water Flows

摘要

Numerical method for the solution of linear boundary value problems for resonantly forced ODE is presented in the present paper. The solution is obtained by the singular value decomposition method. The method is applied to numerical calculation of the coefficients of the complex Ginzburg-Landau equation which describes the development of instability of shallow water flow behind obstacles such as islands. The results of the present study can be applied in practice to control water quality on the sheltered side of islands.