Initial value problem information

calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown...

boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution...

variables as a function of time and of the initial conditions is called the initial value problem. A corresponding problem exists for discrete time situations...

given function of x and t. Initial value problem on (−∞,∞) { u t = k u x x ( x , t ) ∈ R × ( 0 , ∞ ) u ( x , 0 ) = g ( x ) Initial condition {\displaystyle...

or initial point. Since the parameter s {\displaystyle s} is usually time, Cauchy conditions can also be called initial value conditions or initial value...

on a hypersurface in the domain. A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition)...

boundary value problem by reducing it to an initial value problem. It involves finding solutions to the initial value problem for different initial conditions...

gauge of electromagnetism. One method to solve the initial-value problem (with the initial values as posed above) is to take advantage of a special property...

cosmologists to question how the initial density came to be so closely fine-tuned to this 'special' value. The problem was first mentioned by Robert Dicke...

solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have a unique solution...

solution. To verify this prediction, recall the solution of the initial value problem u t t = u x x + u y y , u ( 0 , x , y ) = p ( x , y ) , u t ( 0...

However, this only helps us with first order initial value problems. Suppose we had a linear initial value problem of the nth order: f n ( x ) d n y d x n...

boundary value problems. The method divides the interval over which a solution is sought into several smaller intervals, solves an initial value problem in...

A Riemann problem, named after Bernhard Riemann, is a specific initial value problem composed of a conservation equation together with piecewise constant...

algorithm from numerical analysis and used for the solution of initial value problems. It was introduced in 2001 by Lions, Maday and Turinici. Since then...

well-posed initial value problem. Imposing the condition that our antiderivative takes the value 100 at x = π is an initial condition. Each initial condition...

which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is...

6}A_{1}} We can determine A0 and A1 if there are initial conditions, i.e. if we have an initial value problem. So we have A 4 = 1 4 A 2 = ( 1 4 ) ( − 1 2 )...

c>0} is also known as an exponential function, as it solves the initial value problem f ′ = a f ,   f ( 0 ) = c {\displaystyle f'=af,\ f(0)=c} , meaning...

initial data u ( x , 0 ) = u 0 ( x ) {\displaystyle u(x,0)=u_{0}(x)} . For a nonlinear parabolic PDE, a solution of an initial/boundary-value problem...

that it gives important insights into the dynamics, even if the initial value problem cannot be solved analytically. One example is the planetary movement...

speaking, has a well-posed initial value problem for the first n − 1 {\displaystyle n-1} derivatives. More precisely, the Cauchy problem can be locally solved...

partial differential equation (PDE) of order n that has a well-posed initial value problem for the first n−1 derivatives Hyperbolic plane can refer to: The...

that α is a local solution to the ordinary differential equation/initial value problem α ( t 0 ) = p ; {\displaystyle \alpha (t_{0})=p;\,} α ′ ( t ) =...