fourth order differential equation
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syms f(x)
Df = diff(f,x);
D2f = diff(f,x,2);
D3f = diff(f,x,3);
D4f = diff(f,x,4);
ode =3*D4f+(2*x^2+6)*D3f+5*D2f-Df-2*f == - 4*x^6+ 2*x^5 -55*x^4 - 24*x^3 - 22*x^2 - x*32;
cond1 = f(0)==0;
cond2 = Df(0)==1;
cond3 = D2f(0) == -8;
cond4 = D3f(0) == 6;
conds = [cond1 cond2 cond3 cond4];
fSol(x) = dsolve(ode,conds);
figure
ezplot(fSol(x),[0 1])
The error is :
Warning: Unable to find explicit solution.
> In dsolve (line 201)
(line 13)
Error using inlineeval (line 14)
Error in inline expression ==> matrix([])
Undefined function 'matrix' for input arguments of type 'double'.
Error in inline/feval (line 33)
INLINE_OUT_ = inlineeval(INLINE_INPUTS_, INLINE_OBJ_.inputExpr, INLINE_OBJ_.expr);
Error in ezplotfeval (line 51)
z = feval(f,x(1));
Error in ezplot>ezplot1 (line 486)
[y, f, loopflag] = ezplotfeval(f, x);
Error in ezplot (line 158)
[hp, cax] = ezplot1(cax, f{1}, vars, labels, args{:});
Error in sym/ezplot (line 78)
h = ezplot(fhandle(f),varargin{:});%#ok<EZPLT>
Error in try2 (line 15)
ezplot(fSol(x),[0 1])
采纳的回答
Star Strider
2019-12-31
If an analytical solution is not an option, and a plot of the solution is the objectrive:
syms f(x) X Y
Df = diff(f,x);
D2f = diff(f,x,2);
D3f = diff(f,x,3);
D4f = diff(f,x,4);
ode =3*D4f+(2*x^2+6)*D3f+5*D2f-Df-2*f == - 4*x^6+ 2*x^5 -55*x^4 - 24*x^3 - 22*x^2 - x*32;
% cond1 = f(0)==0;
% cond2 = Df(0)==1;
% cond3 = D2f(0) == -8;
% cond4 = D3f(0) == 6;
[VF,Sbs] = odeToVectorField(ode);
odefcn = matlabFunction(VF, 'Vars',{x,Y});
[X,Y] = ode45(odefcn, [0 1], [0 1 -8 6]);
figure
plot(X, Y)
grid
legend(string(Sbs))
producing:
15 个评论
Star Strider
2019-12-31
kingcruises‘s ‘Answer’ —
I want to plot the solution coming out from this fourth order differential equation
Star Strider
2019-12-31
@kingcruises —
What part of my Answer does not do what you want?
It plots the function and all the derivatives!
kingcruises
2019-12-31
Star Strider
2019-12-31
What does ‘didn’t work’ mean, exactly?
The code I posted ran for me without error and produced the plot I posted. It is simply an extension of your code, using odeToVectorField to produce a column vector of first-order differential equations, and matlabFunction to create an anonymous function that ode45 then integrates to create the plot.
kingcruises
2019-12-31
kingcruises
2019-12-31
Star Strider
2019-12-31
I do not understand the problems you are having with my code.
If you run my code exactly as I wrote it, you should have no problems with it. Note that ‘odefcn’ is the result of odeToVectorField first, followed by matlabFunction. You cannot use a symbolic function with ode45 or any of the other numeric solvers!
The anonymous function ‘odefcn’ is:
odefcn = @(x,Y) [Y(2); Y(3); Y(4); x.*(-3.2e+1./3.0)-((x.^2.*2.0+6.0).*Y(4))./3.0+Y(1).*(2.0./3.0)+Y(2)./3.0-Y(3).*(5.0./3.0)-x.^2.*(2.2e+1./3.0)-x.^3.*8.0-x.^4.*(5.5e+1./3.0)+x.^5.*(2.0./3.0)-x.^6.*(4.0./3.0)];
Just copy that from this Comment and paste it to your script.
Then run it as:
[X,Y] = ode45(odefcn, [0 1], [0 1 -8 6]);
figure
plot(X, Y)
grid
Sbs = {'f' 'Df' 'D2f' 'D3f'};
legend(string(Sbs))
That should work without problems.
kingcruises
2020-1-2
can we get a code with dsolve as my initial code because I have to compare with the MOM "method of moments" solution. As the below figure I have to have the same figure but using dsolve
Star Strider
2020-1-2
Apparently, dsolve cannot integrate your differential equation. (I doubt that an analytic solution exists for it.) That is the reason we went with the numeric integration. The simplify function cannot simplify it to the extent that dsolve can solve it.
kingcruises
2020-1-2
the code works well.
i want dsolve result same as mom solution. I can solve for second order but nor for fourth order
Star Strider
2020-1-2
I do not believe the fourth-order symbolic solution is possible, at least with the functions available in the Symbolic Math Toolbox.
kingcruises
2020-1-2
kingcruises
2020-1-2
kingcruises
2020-1-2
Star Strider
2020-1-2
The ‘method of moments’ was not part of my undergraduate or graduate education. (I had to look it up.) I will leave that part to you.
Plotting the total of the derivatives is straightforward. Only one change to my posted code is needed and that to sum across the columns in the plot call:
[X,Y] = ode45(odefcn, [0 1], [0 1 -8 6]);
figure
plot(X, sum(Y,2))
grid
That should do what you want.
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