97 research outputs found
Stability of approximate factorization with -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 -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
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