Unable to solve the collocation equations -- a singular Jacobian encountered.

Hello everyone,

I'm new to Matlab and have a simple question. I'd like to plot h=x*y, where y takes the form of an ODE. How do I plot h in this x interval, [0,4]?

My code is:

syms y Dy D2y x Y

ode = y-(1/(Dy/y+(D2y*x)/y))^2;

ode1 = solve(ode==0,D2y);

ode2 = matlabFunction(ode1);

odefcn = @(x,y)[y(2);f(y(2),x,y(1))];

bcfcn = @(ya,yb)[ya(1)-2;yb(1)];

xmesh = linspace(0,4,10);

solinit = bvpinit(xmesh, [0 0]);

sol = bvp4c(odefcn,bcfcn,solinit);

plot(sol.x,sol.y(1,:))

Answer 1

[Torsten]

You have an ODE that has a singularity at x=0. Further, solving for D2y leads to two different differential equations. You must decide which is the one you want to solve.

Thus the results below should be treated with care.

syms y Dy D2y x Y 
ode = y-(1/(Dy/y+(D2y*x)/y))^2;
ode1 = solve(ode==0,D2y)

ode1 = 

ode2 = matlabFunction(ode1(1),'Vars',{x,[y Dy]})

ode2 = function_handle with value:
    @(x,in2)(in2(:,1).*(sqrt(1.0./in2(:,1))-in2(:,2)./in2(:,1)))./x

odefcn = @(x,y)[y(2);ode2(x,[y(1),y(2)])];
bcfcn = @(ya,yb)[ya(1)-2;yb(1)];
xmesh = linspace(1e-3,4,10);
solinit = bvpinit(xmesh, [1 1]);
sol = bvp4c(odefcn,bcfcn,solinit);
plot(sol.x,sol.x.*sol.y(1,:))

Warning: Imaginary parts of complex X and/or Y arguments ignored.