- #1
582153236
- 14
- 0
Homework Statement
dx/dt= -x2-2x(1+t+t2)
x(1)=2
estimate x(1.2) with h=0.2
Homework Equations
Implicit Euler:
I was taught that we must solve for yk+1 using Newton's method:
This doesn't seem like it will work because Newton's method assumes a function of only one variable.
According to wikipedia though: The backward Euler method is an implicit method: the new approximation
The Attempt at a Solution
dx/dt= -x2-2x(1+t+t2)
let x(1)=2 be denoted by x0, x(1.2) is denoted by x1
using implicit euler formula:
x1=2+0.2[-x12-2x1(1+1.2+1.22)]
0=2-0.2x12-2.456x1
==> proceed with quadratic formula to solve for x1
My question is whether this method is valid to solve for x1?
Edit: it appears that it is possible to solve for x1 using multivariable Newton's method. This would require finding the inverse matrix of the Jacobian of F.
Last edited by a moderator: