{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

suplecture3

# suplecture3 - Supplemental Lecture 3 Differential Equations...

This preview shows pages 1–6. Sign up to view the full content.

Supplemental Lecture 3 Differential Equations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
III - 2 Differential Equations Let f : R n R . The equation is an n th-order differential equation . = - - 1 1 ) ( , , ) ( ), ( ) ( n n n n dt t x d dt t dx t x f dt t x d
III - 3 Complete Specification To complete the problem, we need to specify initial conditions x (0), dx (0)/ dt , . . . , d n - 1 x (0)/ dt . A solution to the differential equation is a C n function x : R R that satisfies the initial conditions and such that the derivatives satisfy the differential equation for all t . There will be a unique solution to this problem.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
III - 4 Numerical Approximation We can obtain a numerical approximation to the solution as follows. Choose a step size t > 0. x ( i ) ( t ) will be an approximation to d i x ( t )/ dt for i = 0, . . . , n . x (0) ( t ) approximates the solution x ( t ).
III - 5 Computing the Approximation For i = 0, . . . , n , let For j 0, assume we have defined x ( i ) ( j t ).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 15

suplecture3 - Supplemental Lecture 3 Differential Equations...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online