Solving 4th order ode using ode45

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Elayarani M
Elayarani M 2020-9-15
评论： Elayarani M 2020-9-26
How to solve the following 4th order ode using ode45 solver
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Bjorn Gustavsson
Bjorn Gustavsson 2020-9-15
...and aren't you missing one boundary-value?
@madhan - perhaps just as "easy" to use shooting method to find a solution that trails of towads flat at infinity?
Elayarani M
Elayarani M 2020-9-16
Thank you. I will try with that method.

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采纳的回答

Alan Stevens
Alan Stevens 2020-9-15
Here's some coding that basically solves the equation. I've no idea what the value of k should really be, but the constants chosen give a consistent result. The choice of f'''(0) is based on the original equation with the other x=0 values plugged in; where f''(0) is a chosen to give a seemingly reasonable result!
k = -0.002;
xspan = [0 100];
d2fdx20 = -1;
F0 = [0 1 d2fdx20 (1-k*(d2fdx20^2))/(1-2*k)];
[x, F] = ode45(@rates, xspan, F0, [], k);
f = F(:,1);
dfdx = F(:,2);
plot(x, f, x, dfdx),grid
xlabel('x'), ylabel('f and dfdx')
legend('f','dfdx')
function dFdx = rates(x,F,k)
f = F(1);
dfdx = F(2);
d2fdx2 = F(3);
d3fdx3 = F(4);
if x==0
d4fdx4 = 0;
else
d4fdx4 = (d3fdx3 +f.*d2fdx2 - dfdx.^2 - 2*k*dfdx.*d3fdx3 + k*d2fdx2.^2)./(k*f);
end
dFdx = [dfdx; d2fdx2; d3fdx3; d4fdx4];
end
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Bjorn Gustavsson
Bjorn Gustavsson 2020-9-25
Did the numerical solution differ by much? If not then perhaps only numerical deviations? Since you have a non-linear ODE there might be many solutions (right?), have you gotten all analytically? If not then the numerical solution might be one of the other valid solutions.
Elayarani M
Elayarani M 2020-9-26
Thank you Bjorn Gustavsson. First I will try to get all analytic solution and then cross check with the numerical solution.

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