在MATLAB中从2D数组创建函数（在ode45中使用）

Question

I am a first time MATLAB user. I have a 2d array of t vs f in MATLAB. This 2d array correponds to a function, say f(t). I am using ode45 to solve a set of differential equations and f(t) is one of the coefficients ie I have a set of equations of the form x'(t)=f(t)x(t) or variations thereof. How do I proceed?

I need a way to convert my array of t vs f into a function that can be used in the ode45 method. Presumably, the conversion will do some linear interpolation and give me the equation of the best fit curve.

Or if there is another approach, I'm all ears!

Thank you!

Answer 1

This is a simple example with passing function as a parameter to right hand side of the ODE. Create files in the same directory and run main

main.m

t = 0:0.2:10; f = sin(t);
fun = @(xc) interp1(t, f, xc);

x0=0.5
% solve diff(x, t)=sin(t)  
% pass function as parameter                           
[tsol, xsol] = ode45(@(t, x) diff_rhs(t, x, fun),[0.0 8.0], 0.5);

% we solve equation dx/dt = sin(x), x(0)=x0
% exact solution is x(t) = - cos(t) + x(0) + 1
plot(tsol, xsol, 'x');
hold on
plot(tsol, -cos(tsol) + x0 + 1, '-');
legend('numerical', 'exact');

diff_rhs.m

function dx = diff_rhs(t, x, fun)
  dx = fun(t);
end

References in the documentation: interp1 and anonymous Functions .