# Mod Euler Method with two ODEs

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I am trying to create a model the govern bungee jumping and trying to solve nurmerically using mod_euler_method.

We were given equation 1 which is fy in the code and it represent the jumper's acceleration dv/dt

Since equation 1 invovles to unkowns v and y we need a second equation that relates the two is fv which represent dy/dt

function [t, y, v] = modeulerbungee(a, b, n, g, C, K, L)

The code is as follow:

function [t, y, v] = modeulerbungee(a, b, n, g, C, K, L)

%Mod_Euler_method Modified Euler's method

% [t, w, h] = euler_method(f, a, b, alpha, n) performs Modified Euler's method for

% solving the IVP y' = f(t,y) with initial condition y(a) = alpha

% taking n steps from t = a to t = b.

j_ht = 1.75; % Jumper height in Metres

H = 74; % Height of jump point (Metres)

m = 80; % Mass of jumper (Kilograms)

g = 9.8; % Gravitational acceleration (m/s^2)

c = 0.9; % Drag coefficient (Kilogram/Metres)

k = 90; % Spring constant of bungee rope (Newton/Metres)

n = 10000; % Number of iterations

a = 0; % Start time

b = 60; % End time

D = 31; %Height of bridge (Metres)

C = c/m;

K = k/m;

L = 25; %length of rope in metres

h = (b-a)/n; % calculate h

t = a:h:b; % create time array t

% Create function handles for the system of ODE's

fv = @(t, y, v) v;

fy = @(t, y, v) g - C*abs(v)*v - max(0, K*(y - L));

y = zeros(1, n+1); % initialise y array

v = zeros(1, n+1); % initialise v array

% perform modified euler iterations

for i = 1:n

yk1 = h*fv(v(i), y(i));

vk1 = h*fy(v(i),y(i));

yk2 = h*fv(v(i) +yk1, y(i) + yk1);

vk2 = h*fy(v(i) +vk1, y(i) + vk1);

y(i+1) = y(i) + 1/2*(yk1+yk2);

v(i+1) = v(i) + 1/2 * (vk1 + vk2);

end

end

I get an error in Line 30 fv = @(t, y, v) v; and Line 39 yk1 = h*fv(v(i), y(i)); saying their is not enough inputs arguments. I unfortunately don't how to fix it. Thank you and any help will be appreciated

##### 0 Comments

### Accepted Answer

Alan Stevens
on 27 Oct 2021

Like this

%Mod_Euler_method Modified Euler's method

% [t, w, h] = euler_method(f, a, b, alpha, n) performs Modified Euler's method for

% solving the IVP y' = f(t,y) with initial condition y(a) = alpha

% taking n steps from t = a to t = b.

j_ht = 1.75; % Jumper height in Metres

H = 74; % Height of jump point (Metres)

m = 80; % Mass of jumper (Kilograms)

g = 9.8; % Gravitational acceleration (m/s^2)

c = 0.9; % Drag coefficient (Kilogram/Metres)

k = 90; % Spring constant of bungee rope (Newton/Metres)

n = 10000; % Number of iterations

a = 0; % Start time

b = 60; % End time

D = 31; %Height of bridge (Metres)

C = c/m;

K = k/m;

L = 25; %length of rope in metres

h = (b-a)/n; % calculate h

t = a:h:b; % create time array t

% Create function handles for the system of ODE's

fv = @(v, y) v; % You don't need t here as you don't use t in the Euler iterations

fy = @(v, y) g - C*abs(v)*v - max(0, K*(y - L)); % ditto

% Also, make sure your arguments are in the same order here as when you

% call these functios in the modified Euler routine below!

y = zeros(1, n+1); % initialise y array

v = zeros(1, n+1); % initialise v array

% perform modified euler iterations

for i = 1:n

yk1 = h*fv(v(i), y(i));

vk1 = h*fy(v(i),y(i));

yk2 = h*fv(v(i) +yk1, y(i) + vk1);

vk2 = h*fy(v(i) +yk1, y(i) + vk1);

y(i+1) = y(i) + 1/2*(yk1+yk2);

v(i+1) = v(i) + 1/2 * (vk1 + vk2);

end

plot(t, y),grid

##### 2 Comments

Alan Stevens
on 27 Oct 2021

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