recieving error within ODE45: Input arguments to function include colon operator. To input the colon character, use ':' instead.

My code is meant to measure the oscilating path of a pendulum given a series of diferential equations and initial conditions, then the plot the phase plots of the results. However i seem to run into the same error when running the code, the full error message reads: Input arguments to function include colon operator. To input the colon character, use ':' instead.

Error in odearguments (line 75)

y0 = y0(:);

Error in ode45 (line 107)

odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

Error in lab9main (line 46)

[time, sol] = ode45(pos1, [0 tf], angle, opt1);

hope someone can help! thanks!

clc; clear; close all;
fprintf("Nathan Koch\nProject 9\nPendulum project");

Nathan Koch
Project 9
Pendulum project

datetime("today")

ans = datetime
   28-Jul-2023

L = 4.5; %meters
Dtheta_0 = 0; %d(theta_0)
theta_0 = pi / 5.5;
g = 9.81; %m/s
k0 = sin(0.5*theta_0); %parameter of k;
C1 = 0; %drag coef case 1 
C2 = 0.25; %drag coef case 2 


T = @(k,x) 4*sqrt(L/g)*(1./sqrt(1-k.^2*sin(x).^2));%function of k and theta

T0 = @(x) 4*sqrt(L/g)*(1./sqrt(1-k0^2 * sin(x).^2)); %function of theta where k = k0

q = quadgk(T0,0,pi/2); %report value of integral from bounds 
 
fprintf("\n\nthe value of the integral is %.4f\n\n",q);

the value of the integral is 4.3439

%define general equation and initial conditions for use:

angle = @(t) theta_0 + t;

pos1 = @(angle,x) -g/L * sin(angle) - C1*x*abs(x); %second derivative of theta wrt t for case 2

pos2 = @(angle,x) -g/L * sin(angle) - C2*x*abs(x); %second derivative of theta wrt t for case 2

tspan = 0:200;%vector of sample points

tx = 0:0.1:20; %refined points on vector

%Case 1 no drag Cd = 0;
tol = [1e-3, 1e-6];
tf = 200;
print_time = [0, 82.65, 200];

%euler-ing my complex equations

for i = 1:length(tol)
    fprintf("using tolerance of %.3e\n",tol(i))
    for j = 1:length(print_time)
        fprintf("at time step %.2f",print_time(j))
        opt1 = odeset("RelTol",tol(j),"AbsTol",tol(j));
        [time, sol] = ode45(pos1, [0 tf], angle, opt1);
        L1 = interp1(time,sol,print_time(j));
        fprintf("ODE45: %.4f at t = %.4f\n",L1,print_time(j));
    end
    fprintf("\n")
end

using tolerance of 1.000e-03

at time step 0.00

Input arguments to function include colon operator. To input the colon character, use ':' instead.

Error in odearguments (line 75)
y0 = y0(:);

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

for N = 1:length(tol)
    fprintf("using tolerance of %.3e\n",tol(N));
    for M = 1:length(print_time)
        opt2 = odeset("RelTol",tol(M),"AbsTol",tol(M));
        [time, sol] = ode45(pos2, [0 tf], angle, opt2);
        L2 = interp1(time,sol,print_time(M));
        fprintf("ODE45: %,4f at t = %.4f\n",L2,print_time(M));
    end
    fprintf("\n")
end


%Plot the Phase plots for cases 1 and 2
figure(1)
plot(tspan,thet1,'o', tspan,dtheta1,':.')
xlim([0 200])
ylim([0 20])
title('Plot of Oscilations for non linear pendulum (case 1)')

figure(2)
plot(tspan,thet2,'o',tspan,dtheta2,':.')
xlim([0 200])
ylim([0 20])
title('Plot Oscilations for non linear pendulum (case 2)')

Answer 1

[Cris LaPierre]

The specific error is because you are passing in an anonymous function for your initial values rather than values.

Fix this by calling angle at t=0 for your input argument.

[time, sol] = ode45(pos1, [0 tf], angle(0), opt1);

However, that wil just lead to more errors. For example, you are indexing tol using the loop counter for print_time. Since there are more values in print_time than tol, you will get an indexing error from tol(j).

[Nathan]

thank you so much! fixed those errors up and its working now!