Stability of approximate factorization with heta heta -methods

Approximate factorization seems for certain problems a viable alternative to time splitting. Since a splitting error is avoided, accuracy will in general be favourable compared to time splitting methods. However, it is not clear to what extent stability is affected by factorization. Therefore we study here the effects of factorization on a simple, low order method, namely the $theta$-method. For this simple method it is possible to obtain rather precise results, showing limitations of the approximate factorization approach

A note on monotonicity of a Rosenbrock method

AbstractFor a dissipative differential equation with stationary solution u∗, the difference between any solution U(t) and u∗ is nonincreasing with t. In this note we present necessary and sufficient conditions in order for a similar monotonicity property to hold for numerical approximations computed from a Rosenbrock method. Our results also provide global convergence results for some modifications of Newton's method

Numerical Methods -- Lecture Notes 2014-2015

In these notes some basic numerical methods will be described. The following topics are addressed: 1. Nonlinear Equations, 2. Linear Systems, 3. Polynomial Interpolation and Approximation, 4. Trigonometric Interpolation with DFT and FFT, 5. Numerical Integration, 6. Initial Value Problems for ODEs, 7. Stiff Initial Value Problems, 8. Two-Point Boundary Value Problems

Accuracy and stability of splitting with stabilizing corrections

This paper contains a convergence analysis for the method of Stabilizing Corrections, which is an internally consistent splitting scheme for initial-boundary value problems. To obtain more accuracy and a better treatment of explicit terms several extensions are regarded and analyzed. The relevance of the theoretical results is tested for convection-diffusion-reaction equations