Nonstandard finite-difference schemes for general two-dimensional autonomous dynamical systems |
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Institution: | Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA |
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Abstract: | General two-dimensional autonomous dynamical systems and their standard numerical discretizations are considered. Nonstandard stability-preserving finite-difference schemes based on the explicit and implicit Euler and the second-order Runge–Kutta methods are designed and analyzed. Their elementary stability is established theoretically and is also supported by a numerical example. |
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