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In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult they are to solve compared to linear differential equations. This list presents nonlinear ordinary differential equations that have been named, sorted by area of interest.
See also Nonlinear partial differential equation, List of partial differential equation topics and List of nonlinear ordinary differential equations. A–F Name ...
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms.They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture.
Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. [1] Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area ...
Nonlinear programming is the process of solving an optimization problem, where some of the parameters are nonlinear. Nonlinear regression, in statistics, represents fitting a model equation that is not linear in its parameters to the data in a table. Nonlinear resonance in physics is the occurrence of resonance in a nonlinear system.
The nonlinear wave equation is an inhomogeneous differential equation. The general solution comes from the study of ordinary differential equations and can be obtained by the use of a Green's function. Physically one gets the normal electromagnetic wave solutions to the homogeneous part of the wave equation:
The A-stability concept for the solution of differential equations is related to the linear autonomous equation ′ =. Dahlquist (1963) proposed the investigation of stability of numerical schemes when applied to nonlinear systems that satisfy a monotonicity condition.