Conversion to double from sym is not possible

Hello All. I am trying to plot a comparison between the ode45 solution of a simple spring mass equation and the exact solution. The equation is x''=1-(4pi)^2*x My code is below:

%1) Must rewrite 2nd order equation as a system of 1st order equations

clear all

time_period = [0 4];

[t,x]=ode45(@spring,time_period, [0; 0]);

%Call function spring:

% | function dxdt=spring(t,x) |

% | dxdt=[x(2), 1-(4*pi)^2*x(1)]; |

%2)

plot(t,x(:,1));

title('Spring-Mass Function ODE45 Solution')

ylabel('x-position(m)');

xlabel('time(s)');

%3)

x_exact=dsolve('D2x == 1-(16*pi^2)*x', 'Dx(0)=0', 't');

plot(t,x(:,1),'-',t,x_exact(:,1),'--')

title('ODE45 solution vs. Exact Solution');

ylabel('x-position(m)');

xlabel('time(s)');

legend('ODE45','Exact')

The error is in the following line:

plot(t,x(:,1),'-',t,x_exact(:,1),'--')

and it states that conversion from double to sym is not possible. Can anybody help? what am I doing wrong?

Answer 1

[Star Strider]

Defining ‘t’ and other variables as double and then defining them later as symbolic caused those problems. I corrected them so that this has the virtue of working.

You can experiment with it to explore the different properties of the ode45 and Symbolic Math Toolbox solutions:

spring = @(t,x) [x(2); 1-(4*pi).^2.*x(1)];

time_period = [0 4];

[td,xd]=ode45(spring,time_period, [0; 0]);

%Call function spring:

% | function dxdt=spring(t,x) |

% | dxdt=[x(2), 1-(4*pi)^2*x(1)]; |

%2)

plot(td,xd(:,1));

title('Spring-Mass Function ODE45 Solution')

ylabel('x-position(m)');

xlabel('time(s)');

%3)
syms xs(t)

x_exact=dsolve('D2xs == 1-(16*pi^2)*xs', 'Dxs(0)=0', 't')

af_x_exact = matlabFunction(x_exact)

plot(td,xd(:,1),'-',td,af_x_exact(0.007,td),'--')

title('ODE45 solution vs. Exact Solution');

ylabel('x-position(m)');

xlabel('time(s)');

legend('ODE45','Exact')

I created ‘spring’ as an anonymous function because it was more convenient for me.

[Erik]

Thank you for the prompt response. Your help was perfect. All I had to do was apply a 0.25 sec correction to the exact plot and I'm good to go. You are truly a lifesaver and may the karma gods rain good karma down upon thee.

[Star Strider]

My pleasure!

I appreciate your good karma sentiments.