Numerical meths Flashcards
1
Q
A
2
Q
How to improve accuracy of Euler’s method
A
Decrease step length or use midpoint method
(If curve representing particular solution is very concave/convex near point, can be inaccurate)
3
Q
How midpoint method derived
A
Consider gradient of chord joining P0 and P2, approximately gradient of tangent at P1
dy/dx1 = y2-y0/x2-x0 = y2-y0/2h
as h = step length (x1-x0)
4
Q
When estimates aren’t valid
A
If dy/dx undefined at a point, there’s a vertical asymptote
5
Q
Simpsons rule
A
1/3h(endpoints + 4(odd values) + 2(even values)) for 2n strips pf width h
Only works for even number of strips (odd number of points) as derivation is from pairing strips and approximating as a quadratic
find somewhere which goes through parametric
6
Q
A
