Fourth order nonlinear DE solution where forcing function interpolation is known

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Mohammad Ansari 2023-5-21

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评论： John D'Errico 2023-5-22

采纳的回答： Torsten

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!

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Mohammad Ansari 2023-5-21

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 2023-5-22

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

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采纳的回答

Torsten 2023-5-21

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编辑：Torsten 2023-5-21

在 MATLAB Online 中打开

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

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Mohammad Ansari 2023-5-21

Thanks

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MATLAB Mathematics Numerical Integration and Differential Equations Ordinary Differential Equations

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