Fourth order nonlinear DE solution where forcing function interpolation is known

I want to solve the differential equation: , with BCs: (constant).

The function is not explicitly known, but I know its interpolation. I tried fitting a polynomial/exponential, but it I do not get a satisfactory fit. Please help!

[Torsten]

I tried fitting a polynomial/exponential, but it I do not get a satisfactory fit.

What do you need help for ? Fitting f ? Solving the differential equation ? Show what you have done so far.

[Mohammad Ansari]

I just need help with how to use ode45 when I do not know the explicit nonlinear function, but its interpolation. I am sure I can break down the 4th derivative into 4 first order DE's but not sure about what syntax to use for the interpolation.

[John D'Errico]

Sorry. My approach does not apply to a nonlinear forcing term that is a function of the dependednt variable.

Answer 1

[Torsten]

You will have to use bvp4c, not ode45.

And interpolation in the function where you define the derivative function can be done via

fw_inter = interp1(w,fw,y(1))

where w and fw are your data vectors (w ordered) and y(1) is the value of w from bvp4c:

function dydx = bvpfcn(x,y,w,fw)
  fw_inter = interp1(w,fw,y(1));
  dydx = [y(2);y(3);y(4);fw_inter];
end

[Mohammad Ansari]

Thanks