Initial value problem

In mathematics, an initial value problem is a statement of a differential equation together with specified value of the unknown function at a given point in the domain of the solution.

Related Topics:
Mathematics - Differential equation

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Calling the given point t0 and the specified value y0,

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the initial value problem is

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: y'(t) = f(t, y(t)), quad y(t_0) = y_0

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The problem is then to determine the function y.

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This statement subsumes problems of higher order, by interpreting y as a vector.

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For derivatives of second or higher order, new variables (elements of the vector y) are introduced.

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More generally, the unknown function y can take values on infinite dimensional spaces, such as Banach spaces or spaces of distributions.

Related Topics:
Banach space - Distribution

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