Question
In: Math
Problem Four (12 Marks) Use Runge Kutta method of order four to approximate the solution of...
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)
Solutions
milcah answered 2 years agoRelated Solutions
Use the Runge-Kutta method and the Runge-Kutta semilinear method with the indicated step sizes to find...
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]
Use the Runge-Kutta method with step sizes h = 0.1, to find approximate values of the...
Use the Runge-Kutta method with step sizes h = 0.1, to find
approximate values of the solution of
y' + (1/x)y = (7/x^2) + 3 , y(1) = 3/2 at x = 0.5 .
And compare it to thee approximate value of y = (7lnx)/x +
3x/2
Using Runge-Kutta method of order 4 to approximate y(1) with step size h = 0.1 and...
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.
Use 3 steps of the Runge-Kutta (fourth order) method to solve the following differential equation to...
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 the method of order two to approximate the solution to the following initial value problem...
use the method of order two to approximate the solution to the
following initial value problem y'=e^(t-y),0<=t<=1, y(0)=1,
with h=0.5
Use Classic Runge-Kutta method with h = 1 to solve the system y” - y’ -...
Use Classic Runge-Kutta method with h = 1 to solve the
system y” - y’ - 6y = 0, y(0) = 2, y’(0) = 3 on [0,1]
use Runge Kutta 4th order method y'=y-1.3333*exp(0.6x) a) h=2.5 and compare the value to the exact...
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!
Q 4. With the aid of fourth order Runge-Kutta method, solve the competing species model [20...
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.
With the aid of fourth order Runge-Kutta method, solve the competing species model defined by dx/dt...
With the aid of fourth order Runge-Kutta method, solve the
competing species model defined by
dx/dt =x(2 − 0.4x − 0.3y), x(0) = 2
dy/dt =y(1 − 0.1y − 0.3x), y(0) = 4
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.
Write a user-defined MATLAB function that uses classical fourth order Runge-Kutta method to solve a first...
Write a user-defined MATLAB function that uses classical fourth
order Runge-Kutta method to solve a first order ODE problem dydx =
f(x, y) in a given interval a ? x ? b with initial condition y(a) =
y0 and step size of h. For function name and arguments, use [x,y] =
myrk4(f, a, b, h, y0)
Check your function to find the numerical solution for
dydx=?1.2y+7e^(?0.3x) in the interval 0 ? x ? 4 with initial
condition y(0)=3. Run your...
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