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Line 6: Suppose that the [[ordinary differential equation]] :<math> y'(t) = f(t,y(t)), \quad y(t_0)=y_0, </math> is to be solved over the interval <math> [t_0,t_0+ h]</math>. Choose <math>c_k</math> from 0 ≤ ''c''<sub>1</sub>< ''c''<sub>2</sub>< ... < ''c''<sub>''n''</sub> ≤ 1. The corresponding (polynomial) collocation method approximates the solution ''y'' by the polynomial ''p'' of degree ''n'' which satisfies the initial condition <math>p(t_0) = y_0</math>, and the differential equation <math>p'(t_k) = f(t_k,p(t_k)) </math>

Collocation method: Difference between revisions