Search results
Results from the WOW.Com Content Network
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form x ˙ = A ( t ) x , {\displaystyle {\dot {x}}=A(t)x,}
In Itô calculus, the Euler–Maruyama method (also simply called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). It is an extension of the Euler method for ordinary differential equations to stochastic differential equations named after Leonhard Euler and Gisiro Maruyama. The ...
The exact solution of the differential equation is () =, so () =. Although the approximation of the Euler method was not very precise in this specific case, particularly due to a large value step size h {\displaystyle h} , its behaviour is qualitatively correct as the figure shows.
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
Thus it cannot be used directly on purely elliptic partial differential equations, such as Laplace's equation. However, MOL has been used to solve Laplace's equation by using the method of false transients. [1] [8] In this method, a time derivative of the dependent variable is added to Laplace’s equation. Finite differences are then used to ...
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the ...
In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps:
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc. This list presents differential equations that have received specific names, area by area.