In: Advanced Math

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.

(dy /dt) = 1.1ty

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 =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 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...

Use 4 steps of the Modiﬁed Euler’s method to solve the following
diﬀerential equation to t = 2.6, given that y(0) = 1.1. In your
working section, you must provide full working for the ﬁrst two
steps. To make calculations easier, round the calculations at each
step to four decimal places, and provide your ﬁnal answer with four
decimal places. dy/ dt = 1.4sin(ty)

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]

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)

1)Select all that applies to the Fourth-order Runge-Kutta (RK4)
method K subscript
1 equals f left parenthesis t subscript k comma y subscript k
right parenthesis K subscript
2 equals f left parenthesis t subscript k plus h over 2 comma
space y subscript k plus h over 2 space K subscript 1 right
parenthesis K subscript
3 equals f left parenthesis t subscript k plus h over 2 comma
space y subscript k plus h over 2 space K...

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

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!

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.

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- Q1- Explain how industry uses natural gas (cite a specific industry example)? Q2- Why is natural...
- Suppose we are thinking about replacing an old computer with a new one. The old one...
- Read the Medi-Cult Case Study located in the Reading Assignment section. Medi-Cult, a biotech company based...
- Should the management eavesdrop on the telephone or monitor emails? Would an officer be justified in...
- Select an IT industry and discuss what the top uses of databases for this industry are...
- Green Thumb, a manufacturer of lawn care equipment, has introduced a new product. The anticipated demand...
- Dharma Pharmaceuticals Pty Ltd (DPPL) imports a number of pharmaceutical products. In order to hedge its...

ADVERTISEMENT