Rice: Created page with "Category:Differential Equations *Note that this is not tested in MAT22B Numerical solutions of IVPs involve using taylor series and the definition of derivatives: $\frac{dy}{dx}(x=x_0) = \lim_{h\rightarrow 0}\frac{y(x_0+h)-y(x_0)}{h}$ Since we know one initial value of the function, we can use the above property to iteratively approximate the surrounding values with a small step (h). = Classification = Numerical solutions are evaluated by th..."

2024-05-17T21:24:15Z

Created page with "Category:Differential Equations *Note that this is not tested in MAT22B Numerical solutions of IVPs involve using taylor series and the definition of derivatives: <math> \frac{dy}{dx}(x=x_0) = \lim_{h\rightarrow 0}\frac{y(x_0+h)-y(x_0)}{h} </math> Since we know one initial value of the function, we can use the above property to iteratively approximate the surrounding values with a small step (h). = Classification = Numerical solutions are evaluated by th..."

New page

[[Category:Differential Equations]]
*Note that this is not tested in MAT22B

Numerical solutions of [[IVP]]s involve using [[taylor series]] and the definition of derivatives:

<math>
\frac{dy}{dx}(x=x_0) = \lim_{h\rightarrow 0}\frac{y(x_0+h)-y(x_0)}{h}
</math>

Since we know one initial value of the function, we can use the above property to iteratively approximate the surrounding values with a small step (h).

= Classification =

Numerical solutions are evaluated by three criterias:
# ''Convergence'' checks if the solution is correct as h approaches 0
# ''Accuracy'' measures how good the approximation is
# ''Stability'' I am not very familiar with.

Accuracy is measured by ''order'' of h in the error. A higher order usually means that with each reduction in h, there is a greater increase in accuracy.

Numerical solutions of differential equations - Revision history