Seminário de Análise Numérica e Otimização: Order reduction phenomenon when integrating PDEs with Strang method

Exponential splitting methods, and in particular Strang method, are frequently used in the literature for integrating differential equations. These kind of methods are interesting when the numerical integration of separated parts of the equation is cheaper or easier than the numerical integration of the whole equation. In this talk, we will see how this property is an advantage for the numerical integration of the nonlinear Schr ̈odinger equation (NLSE). However, we will show that, despite the advantages of splitting methods, there is a possible drawback when considering non homogeneous boundary conditions. This is the order reduction that is observed in practice. Then, we will propose a technique to avoid order reduction and whose computational cost is negligible compared to the cost of the method.