Oscillation of θ-methods for the Lasota-Wazewska model
The aim of this paper is to discuss the oscillation of numerical solutions for the Lasota-Wazewska model. Using two θ-methods (the linear θ-method and the one-leg θ-method), some conditions under which the numerical solutions oscillate are obtained for different range of θ. Furthermore, it is shown that every non-oscillatory numerical solution tends to the fixed point of the original continuous equation. Numerical examples are given.
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