Numerical integration of \((2+1)\) dimensional PDEs for \(S^2\) valued functions
The authors compare differential numerical methods of studying the time evolution of partial differential equations (PDEs) in the \((2+1)\)-dimensional \(S^2\) sigma model. They use three different methods to describe the fields: a unit length vector, the polar angles, and a complex field. For the time integration, they employ both a fourth-order Runge-Kutta method and the leapfrog method. For each formulation, they tackle the problems created by the field description and develop a stable method to solve the equations satisfied by the fields. They compare the results of all methods, focussing their attention on the accuracy of the results and the computing requirement.
scientific article; zbMATH DE number 1212281