Backward error analysis has become an important tool for understanding the long time behavior of numerical integration methods. This is true in particular for the integration of Hamiltonian systems ...

Parabolic partial differential equations (PDEs) are fundamental in modelling a wide range of diffusion processes in physics, finance and engineering. The numerical approximation of these equations ...

Numerical Solution of Systems of Linear Equations, Iterative Methods Formulation and analysis of basic stationary methods e.g. Gauss-Jacobi, Gauss-Seidel. The numerical solution of Poisson's equation.

These estimates are applicable to a more general class of integration methods and, in many cases, are better than those of Wielandt. For every eigenvalue, a numerical solution for the corresponding ...