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

Question

jcn2912 2017-12-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/371134-i-need-help-with-this-problem-finite-difference-method-and-ode

回答： Torsten 2017-12-5

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')