In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless...

loose rule of thumb dictates that stiff differential equations require the use of implicit schemes, whereas non-stiff problems can be solved more efficiently...

sometimes used to refer to the coupling stiffness. It is noted that for a body with multiple DOF, the equation above generally does not apply since the...

solving this equation. The direct stiffness method forms the basis for most commercial and free source finite element software. The direct stiffness method...

geochemistry, a way of displaying water chemistry data Stiff equation, an ordinary differential equation that exhibits behaviour at two widely different scales...

map. Schröder's equation Stiff equation Lorenz, Edward N. (1964-02-01). "The problem of deducing the climate from the governing equations". Tellus. 16 (1):...

Newton–Laplace equation: c = K s ρ , {\displaystyle c={\sqrt {\frac {K_{s}}{\rho }}},} where K s {\displaystyle K_{s}} is a coefficient of stiffness, the isentropic...

creating the equation of state such as phase transitions. Another aspect of the equation of state is whether it is a soft or stiff equation of state. This...

of the above equation leads to computing the deflection of the beam, and in turn, the bending stiffness of the beam. Bending stiffness in beams is also...

stable method when solving a stiff equation. Yet another definition is used in numerical partial differential equations. An algorithm for solving a linear...

elliptic partial differential equations, the stiffness matrix is a matrix that represents the system of linear equations that must be solved in order to...

approximation. These methods are especially used for the solution of stiff differential equations. The methods were first introduced by Charles F. Curtiss and...

sides of the equation, and thus the method needs to solve an algebraic equation for the unknown y k + 1 {\displaystyle y_{k+1}} . For non-stiff problems,...

very good at integrating stiff equations. Hairer, Ernst; Wanner, Gerhard (1996), Solving ordinary differential equations II: Stiff and differential-algebraic...

of order 2 to 6; especially suitable for stiff equations Numerov's method — fourth-order method for equations of the form y ″ = f ( t , y ) {\displaystyle...

applied to stiff equations. Consider the linear test equation y ′ = λ y {\displaystyle y'=\lambda y} . A Runge–Kutta method applied to this equation reduces...

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves...

multistep methods on stiff equations, consider the linear test equation y' = λy. A multistep method applied to this differential equation with step size h...

where C i j k l {\displaystyle C_{ijkl}} is the stiffness tensor. These are 6 independent equations relating stresses and strains. The requirement of...

numerically unstable, especially for stiff equations, meaning that the numerical solution grows very large for equations where the exact solution does not...

bending equation: M = − E I d 2 w d x 2 . {\displaystyle M=-EI{d^{2}w \over dx^{2}}.} The dynamic beam equation is the Euler–Lagrange equation for the...

mass density of a material. It is also known as the stiffness to weight ratio or specific stiffness. High specific modulus materials find wide application...

example, an elastic pendulum whose spring's stiffness does not exactly obey Hooke's law. The Duffing equation is an example of a dynamical system that exhibits...

numerical computations with interval inclusions, differential equations and stiff equations, astronomical functions, geometry, and more. The clean interface...

Originally developed for solving stiff differential equations, the methods have been used to solve partial differential equations including hyperbolic as well...

certain equation that I will call the "characteristic equation", the degree of this equation being precisely the order of the differential equation that...

where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring...

the above equation), and they can be much harder to implement. Implicit methods are used because many problems arising in practice are stiff, for which...

differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to...

Arterial stiffness occurs as a consequence of biological aging and arteriosclerosis. Inflammation plays a major role in arteriosclerosis development,...