"Is u˙h(t0+th)=∑j=1⋯su˙h(t0+cjh)Lj(t) true interpolation formula?" was answered by our community

Christopher Stone

Answered question

2022-04-16

{\dot{u}}_{h} (t_{0} + t h) = \sum_{j = 1 \dots s} {\dot{u}}_{h} (t_{0} + c_{j} h) L_{j} (t)

true interpolation formula?

tempur8x43

Beginner2022-04-17Added 16 answers

Since

u_{h} (x)

is a polynomial of degree s, then the polynomial

u_{h} (t_{0} + t h)

is a polynomial of degree s by t. In this way, the polynomial

{\dot{u}}_{h} (t_{0} + t h) = \frac{\partial}{\partial t}, u_{h} (t_{0} + t h)

is a polynomial of degree

(s - 1)

, which can be presented as a Lagrange interpolation polynomial with the nodes

t_{0} + c_{1} h, t_{0} + c_{2} h, \dots, t_{0} + c_{s} h,

, which can be presented as a Lagrange interpolation polynomial with the nodes

t_{0} + c_{1} h, t_{0} + c_{2} h, \dots, t_{0} + c_{s} h,

i.e. in the form (1).

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