Nonstandard discrete approximations preserving stability properties of continuous mathematical models

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Abstract

Most numerical methods for differential equations introduce spurious solutions. Westudy the method presented by Mickens to obtain exact nonstandard methods for some ordinary differential equations. We show how to generalize his method to equations with no known exact analytical solution, and show that the new scheme has better stability properties than Runge-Kutta methods. We apply the method to several examples. © 2004 Elsevier Ltd. All rights reserved.

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Solis, F. J., & Chen-Charpentier, B. (2004). Nonstandard discrete approximations preserving stability properties of continuous mathematical models. Mathematical and Computer Modelling, 40(5–6), 481–490. https://doi.org/10.1016/j.mcm.2004.02.028

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