I need help, How to solve bvp4c error?
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Hello, I want to solve the following bvp using bvp4c:
- The differential equation is: y''''(x)-A(x)y''(x)+B(x)y(x)=f(x)with the boundary conditions: y(0)=y'(0)=0 and y(200)=y'(200)=0
- The coefficients are:
- f(x)=diff(psi,4,'x')*(-2*alpha*exp(-alpha*x)) +diff(psi,3,'x')*(6*alpha^2*exp(-alpha*x))++diff(psi,2,'x')*exp(-alpha*x)*(2*1i*alpha^2*diff(psi,'x')-4*alpha^3)-4*alpha^3*exp(-alpha*x)
- A(x)=(2*alpha^2+1i*alpha*diff(psi,'x')) and B(x)=(alpha^4+1i*(alpha^3*diff(psi,'x') +alpha*diff(psi,3,'x'))).
- were the parameter psi is a known function of x and alpha is a unknown constant parameter.
- I rewrite the differential equation as a system of first order equations of the form dydx=F(x,y).
- I use the following code:
- function dydx=stream(x,y,psi,alpha) % stream = EDO/BVP the streamfunction corresponding to a turbulent gaz flow % dydx = stream(x,y psi,alpha) evaluates derivative.
- dydx=[y(2) y(3) y(4) diff(psi,4,'x')*(-2*alpha*exp(-alpha*x)) +diff(psi,3,'x')*(6*alpha^2*exp(-alpha*x))+diff(psi,2,'x')*exp(-alpha*x)*(2*1i*alpha^2*diff(psi,'x')-4*alpha^3)-4*alpha^3*exp(-alpha*x)+(2*alpha^2+1i*alpha*diff(psi,'x'))*y(3)-(alpha^4+1i*(alpha^3*diff(psi,'x')+alpha*diff(psi,3,'x')))*y(1)];
- end
- function res = streambc(ya,yb,~)% streambc ODE/BVP streamfuction boundary conditions.% res = streambc(ya,yb) evaluates residual.
- res=[ya(1);ya(2);yb(1);yb(2)];
- end
- function yinit = streaminit % streaminit ODE/BVP streamfuction initial guess.% yinit= streaminit(x) evaluates initial guess at x.
- yinit=[0;1;0;-1];
- solinit=bvpinit(linspace(0,200,101),@streaminit);
- sol= bvp4c(@courant,@streambc,solinit);
- x=linspace(0.0,200,101);
- y = deval ( sol, x );
- plot ( x, y(1,:) );
- end
- by running this code, a message appears: "Not enough input arguments"I don't know what I could add as input arguments! Could you please help me understand and solve the problem? I will be very grateful.
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Answers (1)
Torsten
on 7 Jan 2015
1. You pass a handle called "courant" to bvp4c, but you supply the derivatives in a function called "stream".
2. If you want to pass psi and alpha to stream, the call to bvp4c must read sol=bvp4c(@(x,y)stream(x,y,psi,alpha),@streambc,solinit);
Best wishes
Torsten.
3 Comments
Torsten
on 8 Jan 2015
Of course the lines
solinit=bvpinit(linspace(0,200,101),@streaminit);
sol= bvp4c(@courant,@streambc,solinit);
x=linspace(0.0,200,101);
y = deval ( sol, x );
plot ( x, y(1,:) );
have to be outside the function streaminit.
Did you take this into account ?
Best wishes
Torsten.
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