MATLAB: Fixed time step for ODE45

Question

Hi,

aakash here.

I have written the code below to solve the second order ODE using ODE45. There is an event condition in my code. Because of presence of this event condition, I am not (i dont know) able to use fixed time step in ODE45. Can somebody please help me with this. I request all to please help me to add the fixed time step in this code.

Waiting for the responses.

Thank you

~aakash

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc

clear all

close all

global k Th0 e m c t

%% Input parameters (Length (L), co-efficient of restitution (e), acceleration due to gravity (g))

e=0.9; m=1; c=0; k=246.46;

%% Initial condition

Thid = 8*40/(5*pi)^3; % position from where the mass is released

Thiv = 0; % inital velocity (at t=0)

Th0 = 0.05; % Position where the wall is there

tfi = 5; % time final time

%% ode45 (function call)

eta0=[Thid Thiv]; % Initial conditions

tspan=[0 tfi];

options = odeset('Events',@aakash_function);

t_vec = [];

eta_vec = [];

tcon=0;

ii=1;

while tcon<tfi %% to check whether final time is reached or not

tspan=[tcon tfi];

[t,eta] = ode45(@aakash_mass,tspan,eta0,options);

eta0=[eta(end,1) -(e*eta(end,2))]; %% modified inital conditions after impact

tcon=t(end,1);

t_vec = [t_vec;t];

eta_vec = [eta_vec;eta];

end

t_vec = [t_vec;t];

eta_vec = [eta_vec;eta];

%%

syms u5 x

u5 = sin(5*pi*x)*eta_vec(:,1)

%% Plot

% close all

for i = 1:length(u5)

fig = ezplot(u5(i))

set(fig,'Linewidth',1.5)

xlim([0 1])

ylim([-0.25 0.25])

grid on

title('only third mode')

pause(0.0000000000001)

end

Answer 1

If you are only concerned about output at fixed time-step, then you can pass tspan as a vector of time-values

tspan= tcon:0.01:tfi;
[t,eta] = ode45(@aakash_mass,tspan,eta0,options);