Content deleted Content added
m →Ordinary differential equations: "coefficient" to "coefficients" in last paragraph |
|||
Line 5:
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+c_k 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>
| |||