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Fractional differential equations as alternative models to nonlinear differential equations
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Bonilla +3 more
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A note on discretization of nonlinear differential equations
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2002An important issue when integrating nonlinear differential equations on a digital computer is the choice of the time increment or step size. For example, it is known that if this quantity is not sufficiently short, spurious chaotic motions may be induced when integrating a system using several of the well-known methods available in the literature.
Eduardo M. A. M., Mendes +1 more
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Nonlinear Differential Equations
2014We now turn our attention to the initial-value problem for a nonlinear differential equation of the form $$ \dot{x}\left( t \right) = f\left( {t,x\left( t \right)} \right),\quad x\left( \tau \right) = \xi ,\quad \left( {\tau ,\xi } \right) \in J \times G, $$ where \( J \subset {\mathbb{R}} \) is an interval, G is a non-empty open subset of ...
Hartmut Logemann, Eugene P. Ryan
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Nonlinear Differential Equations
1997Traditionally all the macroscopic phenomena observed in nature have been studied via solutions of differential equations which are described by smooth and continuous curves. This approach works very well for a class of problem like the planetary motion where the orbits are regular geometric objects (namely, ellipsi).
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Nonlinear Differential Equations
2016This chapter explicitly discusses nonlinear systems of ODE using linear approximation methods. Each system has equilibrium points associated with it and an related linear system of ODE governed by the linear dynamics determined by the Jacobian at the given equilibrium.
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