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Differential Identities for Nonlinear Partial Differential Equations
Journal of Mathematical Sciences, 2016Summary: We obtain new algebraic analytic presentations for solutions and coefficients of nonlinear second order differential equations and systems of such equations.
Anikonov, Yu. E., Neshchadim, M. V.
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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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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
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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Differential Equations: Linearity vs. Nonlinearity
SIAM Review, 1963Hale, J. K., LaSalle, J. P.
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Nonlinear Differential Equations.
The American Mathematical Monthly, 1963W. T. Kyner, Raimond A. Struble
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Method for Finding Highly Dispersive Optical Solitons of Nonlinear Differential Equations
Optik, 2020Nikolay A Kudryashov
exaly