Collocation method: Difference between revisions

Revision as of 21:08, 7 June 2011

Revision as of 10:17, 12 March 2012

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where ''y''₁ = ''p''(''t''₀ + ''h'') is the approximate solution at ''t'' = ''t''₀ + ''h''.

This method is known as the "[[trapezoidal rule. (differential equations)|trapezoidal rule]]" for differential equations. Indeed, this method can also be derived by rewriting the differential equation as

:<math> y(t) = y(t_0) + \int_{t_0}^t f(\tau, y(\tau)) \,\textrm{d}\tau, \, </math>