Suppose that we use the Improved Euler's method to approximate the solution to the differential equation dy y(0.5) = 2. dz Let f(x, y) = x-ly. We let zo = 0.5 and yo = 2 and pick a step size h = 0.25. The improved Euler method is the the following algorithm. From (2n, yn), our approximation to the solution of the differential equation at the n-th stage, we find the next stage by computing the x-step n+1=n+h, and then k₁, the slope at (m, n). The predicted new value of the solution is Zn+1 = yn + h.k₁. Then we find the slope at the predicted new point k₂ = f(n+1, 2+1) and get the corrected point by averaging slopes Complete the following table: n En Yn Ki Zn+1 kq 0 0.5 2 -1.51.625-0.875 T 2 3 - ly; 4 h Yn+1 = yn +(1+k₂). The exact solution can also be found for the linear equation. Write the answer as a function of . y(x) = 0 Thus the actual value of the function at the point = 1.5 is y(1.5) =
Suppose that we use the Improved Euler's method to approximate the solution to the differential equation dy y(0.5) = 2. dz Let f(x, y) = x-ly. We let zo = 0.5 and yo = 2 and pick a step size h = 0.25. The improved Euler method is the the following algorithm. From (2n, yn), our approximation to the solution of the differential equation at the n-th stage, we find the next stage by computing the x-step n+1=n+h, and then k₁, the slope at (m, n). The predicted new value of the solution is Zn+1 = yn + h.k₁. Then we find the slope at the predicted new point k₂ = f(n+1, 2+1) and get the corrected point by averaging slopes Complete the following table: n En Yn Ki Zn+1 kq 0 0.5 2 -1.51.625-0.875 T 2 3 - ly; 4 h Yn+1 = yn +(1+k₂). The exact solution can also be found for the linear equation. Write the answer as a function of . y(x) = 0 Thus the actual value of the function at the point = 1.5 is y(1.5) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that we use the Improved Euler's method to approximate the solution to the differential equation
dy
y(0.5) = 2.
dz
Let f(x, y) = x-ly.
=
We let zo = 0.5 and yo2 and pick a step size h = 0.25. The improved Euler method is the the following algorithm.
From (2n, yn), our approximation to the solution of the differential equation at the n-th stage, we find the next stage
by computing the x-step n+1 = n+h, and then k₁, the slope at (m, n). The predicted new value of the solution
is Zn+1 = yn + h.k₁. Then we find the slope at the predicted new point k₂ = f(n+1, 2+1) and get the corrected
point by averaging slopes
Complete the following table:
n En Yn Ki Zn+1 K₂
0 0.5 2 -1.51.625-0.875
T
2
3
- ly;
4
h
Yn+1 = Yn+(k1+k₂).
The exact solution can also be found for the linear equation. Write the answer as a function of .
y(x) = 0
Thus the actual value of the function at the point = 1.5 is
y(1.5) =
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