Post-projected Runge-Kutta methods for index-2 differential-algebraic equations
The present paper deals with numerical methods for index-2 differential algebraic equations in Hessenberg form, that is, \[ y'(x)= f(y(x), z(x)),\quad 0= g(y(x)) \] with \(Dg(y){\partial f\over\partial z} (y,z)\) invertible. The authors introduce a slight modification of the widely used projected Runge-Kutta methods. In the so-called post-projected Runge-Kutta methods the projection step is applied only whenever an output is required. It is shown that in most cases the order of convergence of post-projected methods is the same as for projected Runge-Kutta methods. Finally, numerical examples are presented.
index-2 differential algebraic equations
scientific article; zbMATH DE number 1787724