Proof of Formulae Used to Solve Differential Equations Numerically

It's only fair to share...Share on FacebookTweet about this on TwitterPin on PinterestShare on Google+Share on RedditEmail this to someone

The Taylor series for a function expanded about a pointis

We can derive two very useful series, evaluated atand



(1)-(2) gives (3)

(1)+(2) gives(4)

(3) and (4) may be used to solve second order differential equations numerically at any point, given any two boundary conditionsandWrite


Then (3) becomes and (4) becomes

We can substitute this, withinto the second order differential equationto obtain

This equation is rearranged to makethe subject:

Givenandand a functionwe can find

Comments are closed.