Use the Runge-Kutta method and the Runge-Kutta semilinear method
with the indicated step sizes to find approximate values of the
solution of the given initial value problem at 11 equally spaced
points (including the endpoints) in the interval. This question is
from the differential equation.
y'-4y = x/y^2(y+1) , y(0) = 1; h=0.1, 0.05 , 0.025, on [0,
1]
Using Runge-Kutta method of order 4 to approximate y(1) with
step size h = 0.1 and h = 0.2 respectively (keep 8 decimals):
dy/dx = x + arctan y, y(0) = 0.
Solutions: when h = 0.1, y(1) = 0.70398191. when h = 0.2, y(1) =
0.70394257.
Problem Four
Use Runge Kutta method of order four to approximate the solution
of the initial value problem
?′ + 2? = ??3?, 0 ≤ ? ≤ 1, ?(0) = 0, ???ℎ ℎ = 0.5
Hint: Compute ?(0.5) ??? ?(1)
use Runge Kutta 4th order method
y'=y-1.3333*exp(0.6x)
a) h=2.5 and compare the value to the exact value
b) h=1.25 and compare the value to the exact value
Thks!
Use 3 steps of the Runge-Kutta (fourth order) method to solve
the following differential equation to t = 2.4, given that y(0) =
2.3. In your working section, you must provide full working for the
first step. To make calculations easier, round the tabulated value
of y at each step to four decimal places.
a) Provide the four K-values that are calculated at the first step,
with four decimal places. b) Provide your answer for y(2.4) with
four decimal places....
Use eulers Method with step size h=.01 to approximate the
solution to the initial value problem y'=2x-y^2, y(6)=0 at the
points x=6.1, 6.2, 6.3, 6.4, 6.5
Use Euler's method with step size 0.5 to compute the approximate
y-values y1, y2,
y3 and y4 of the solution
of the initial-value problem. y' = y − 5x, y(3) = 1.
y1 = ______
y2 =______
y3 =_______
y4=________
Please show all work, neatly, line by line and justify steps so
that I can learn.
Thank you!
Q 4. With the aid of fourth order Runge-Kutta method, solve
the competing species model
[20 points]
defined by
dx =x(2 − 0.4x − 0.3y), x(0) = 4 dt
dy =y(1 − 0.1y − 0.3x), y(0) = 3 dt
where the populations x(t) and y(t) are measured in thousands
and t in years. Use a step size of 0.2 for 0 ≤ t ≤ 2 and plot the
trajectories of the populations with Matlab or GNU Octave.