Nonlinear Behaviour of Time-stepping Algorithms for Initial Value Problems
نویسنده
چکیده
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed out through diagrams or maps of computed asymptotic solutions in a suitable parametric space. Applying this methodology to a nonlinear test equation, we compared some numerical features of the well known second-order CrankNicolson solver with those of a recent proposed version which is fourth-order accurate. The approach gives some useful indication on the capabilities of familiar and innovative ODE integrators when applied to nonlinear problems. CISETecnologie Innovative, Applied Mathematics Section Via Reggio Emilia 39 20090 Segrate MILANO (Italy) Tel. 39+2+21672216 Fax 39+2+21672620 E-mail [email protected]
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