Ad
related to: non linear non homogeneous differential equation
Search results
Results from the WOW.Com Content Network
Differential equations are prominent in many scientific areas. 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.
Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]
A non-linear differential equation is a differential equation that is not a linear equation in the unknown function and its derivatives (the linearity or non-linearity in the arguments of the function are not considered here).
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]
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 .
A loose rule of thumb dictates that stiff differential equations require the use of implicit schemes, whereas non-stiff problems can be solved more efficiently with explicit schemes. The so-called general linear methods (GLMs) are a generalization of the above two large classes of methods.
Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are solutions of linear differential equations (see Holonomic function). When physical phenomena are modeled with non-linear equations, they ...
Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation
Ad
related to: non linear non homogeneous differential equation