We are trying to use ode45 to solve for function Q1, this is my code and the error that i keep getting. Can i please get some help on what to fix?

clc;clear;close all;
t0 = -10:10;
y0 = pi:3*pi;
ode45(@Q1,t0,y0)
% Louis is creating the function dP. work out,
function [dP dWout] = Q1(dV,theta)
%setting all known varibales defining each
gamma = 1.4; R = 287; r = 8.4; L = 12; S = 8; V0 = 50; b = 9; T1 = 300;
theta_s = 3*pi/2; theta_b = pi; q_in = 2.8*10^6; Tw = 300; p = 1.013e5;E = 8/(2*12);
dV= dv(theta);
% dV = diff(V(theta),1);
% dv = dV(theta)
%Louis is defining the function dP in terms of theta
dP = gamma*(p*dV)/(V(theta));
dP = dP(:,1);
%defining the function work out in terms of theta
dWout = p*dV;
end
%setting the function to calculate the derivative of Volume in terms of
%theta.
function VolumeDer = dv(theta)
VolumeDer = diff(V(theta),1);
end
%Defining the Temeprature function in terms of theta.
function Tspan = T(theta,C)
gamma = 1.4; R = 287; r = 8.4; L = 12; S = 8; V0 = 50; b = 9; T1 = 300;
theta_s = 3*pi/2; theta_b = pi; q_in = 2.8*10^6; Tw = 300; p = 1.013e5;E = 8/(2*12);
Tspan = (p*V(theta))/((M(C,theta))*(R));
end
%defining our mass function in terms of theta
function mass = M(C,theta)
gamma = 1.4; R = 287; r = 8.4; L = 12; S = 8; V0 = 50; b = 9; T1 = 300;
theta_s = 3*pi/2; theta_b = pi; q_in = 2.8*10^6; Tw = 300; p = 1.013e5; E = 8/(2*12);
mass = M0*exp(-C/w)*(theta-pi);
end
function Volume = V(theta)
gamma = 1.4; R = 287; r = 8.4; L = 12; S = 8; V0 = 50; b = 9; T1 = 300;
theta_s = 3*pi/2; theta_b = pi; q_in = 2.8*10^6; Tw = 300; p = 1.013e5;E = 8/(2*12);
Volume = V0*(1+((r-1)/(2*E))*(1+E*(1-cos(theta))-sqrt(1-E.^2*(sin(theta)).^2)));
end

THIS IS THE ERROR THAT I KEEP GETTING

Error using odearguments

Q1 returns a vector of length 6, but the length of initial conditions vector is 7. The vector

returned by Q1 and the initial conditions vector must have the same number of elements.

Error in ode45 (line 107)

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

Error in P2Q1Test (line 8)

ode45(@Q1,t0,y0)

[Star Strider]

Reference — We are trying to solve Q1 using ode45 and these are my functions and my error that i am giving, is there any help that yall can do?

Answer 1

[Walter Roberson]

y0 = pi:3*pi

y0 = 1×7

3.1416 4.1416 5.1416 6.1416 7.1416 8.1416 9.1416

7 initial conditions

dV= dv(theta);

That are passed to dv

VolumeDer = diff(V(theta),1);

which uses the diff() operation on them. The diff() operation is numeric differences -- x(2:end)-x(1:end-1) . The diff() operation is not derivatives -- not unless V(theta) returns a symbolic results or symbolic function result.

The size of the output for numeric diff() is one smaller in the dimension being operated on (unless second or more differences are requested) so with the input being length 7, the output is length 6.

And then you use that vector of length 6 to calculate the results of the function -- so you are going to return a vector of length 6 when you need a vector of length 7.

[Walter Roberson]

syms theta
dv = simplify(diff(V(theta), theta))

dv = 

That should be your dv, not numeric differences.

function Volume = V(theta)
gamma = 1.4; R = 287; r = 8.4; L = 12; S = 8; V0 = 50; b = 9; T1 = 300;
theta_s = 3*pi/2; theta_b = pi; q_in = 2.8*10^6; Tw = 300; p = 1.013e5;E = 8/(2*12);
Volume = V0*(1+((r-1)/(2*E))*(1+E*(1-cos(theta))-sqrt(1-E.^2*(sin(theta)).^2)));
end

[Walter Roberson]

I recommend that you set up your system using Symbolic Toolbox, and that you then follow the workflow shown in the first example for odeFunction in order to create a function handle to be passed to ode45()