In a recent post onsolving ODEs, the reader Jason wondered if there was a way to do away with the manual algebraic steps usingSymbolic Math Toolbox。目前不是罐头的方法所以the result is a MATLAB program, but you can do so inMuPAD符号数学工具箱,象征性的引擎。For now, I want to show you how you might generate the ODE solution in the case where MuPAD finds a closed-form solution.

Contents

Define Symbolic Variables

Let's first define the variables we need to describe the equations for a simple harmonic oscillator, using the same notation as the post linked above.

symsxtmk

Solve the System

Using the functiondsolve, we find the solution.

sol = dsolve('m*D2x+k*x(t)','x(0) = 0','Dx(0) = 1','t');

Reformat the solution display suitable for posting.

csol = char(sol); disp(csol(1:45)) disp(csol(46:end))

(m*exp((t*(-k*m)^(1/2))/m))/(2*(-k*m)^(1/2)) - m/(2*exp((t*(-k*m)^(1/2))/m)*(-k*m)^(1/2))

Convert Solution from MuPAD

UsingmatlabFunction, I next generate a function handle to a MATLAB version of the solution.

f = matlabFunction(sol);

Again, reformat expression to display more nicely in post.

cf = func2str(f); disp(cf(1:65)) disp([' ', cf(66:end)])

@(k,m,t)m.*exp((t.*sqrt(-k.*m))./m).*1.0./sqrt(-k.*m).*(1.0./2.0) -m.*exp(-(t.*sqrt(-k.*m))./m).*1.0./sqrt(-k.*m).*(1.0./2.0)

Set Values for Mass and Spring Constant

I'm using the same values forkandmthat I used in the referenced post.

k = 10; m = 1;

I'm now creating a short-hand function with the values forkandmset so I can plot the result.

fnew = @(t) f(k,m,t);

Plot the Solution

t = 0:0.01:10; plot(t,fnew(t))

All Well and Good IF ...

That's all well and good if MuPAD can find an analytic solution to the differential equation. For now, there is not a way to automatically generate a MATLAB program for the system of equations defining the ODE suitable for solving numerically. MuPAD itself has numerical ODE solvers which may be suitable. Do you have problems that straddle the symbolic and numerical worlds? How do you handle them? Let me knowhere。

Get the MATLAB code

Published with MATLAB® 7.10