I need help with this problem (finite difference method and ode)

Hello, I solved this question using ode45. But I'm having trouble solving for y(t) using finite difference method. Here is the code I have so far. Can you explain to me how to use finite difference method on this problem? Thanks.

clear all

close all

c=0.0001;

g=9.81;

%dy/dt=v

%dv/dt=-cv^3-g

%ODE system dy_dt=F(t,y)

F = @(t,y) [y(2);-c*(y(2))^3-g];

%dy-dt=f(t,y)

f = @(t,y) -y;

%initial conditions

y0 = [40;0];

%Numerical solution using ode45 

[t,yNumerical]=ode45(F,[0 5],y0);

%Analytical Solution

figure

plot(t,yNumerical(:,1),'--o','LineWidth',2)

hold on

plot(t,yNumerical(:,2),'--o','LineWidth',2)

legend('Position','Velocity')

Answer 1

[Torsten]

How do you know that dy/dt at t=0 has to be 0 in order to reach a height of 5 m after 5 seconds ?

Hint: "ODE45" is not the correct solver for this problem, but "bvp4c".

For a finite-difference solution see

http://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node9.html

Best wishes

Torsten.