ode23 and ode45 problem

Suppose we have a differential equation dy/dx=-2x+4y^2 over the range x=0 to 1 with y(0)=0. I need to solve this question with 'ode23' and ode45 in matlab. Does anybody help me?

[John D'Errico]

Next time, why not make an effort to do your homework yourself? Then show what you tried and ask for someone to help fix it, if you do not succeed.

[baran erbas]

Because i have no idea about this question if you can give me an example solution i will try to solve my question.

Answer 1

[Stephan]

% Solve symbolic (blue line in plot)
syms y(x) x
eqn = diff(y,x) == -2*x+4*y^2
sol_symbolic = dsolve(eqn,y(0)==0);
fplot(sol_symbolic,[0 1])
hold on

% solve numeric with ode45 (red dots in plot)
[V, S] = odeToVectorField(eqn);
fun = matlabFunction(V,'vars', {'x','Y'});
[x, sol_numeric] = ode45(fun,[0 1], 0);
plot(x, sol_numeric,'or')
hold off

With this example code it should be possible to use ode23 also

[baran erbas]

thank you

[baran erbas]

function xl=H(x,y)

xl=zeros(2,1);

xl(1)=x(2);

xl(2)=-2*x+4*y^2;

[y,x]=ode45['H',[0,1],[0,1]];

I tried this but i think it is totally wrong. I should write this code like this. how can i do like that??

[Jan]

Almost nice.

function main
[y,x] = ode45(@H, [0,1], [0,1]);
%            ^                ^ round parentheses
end

function xl = H(x,y)
xl    = zeros(2,1);
xl(1) = x(2);
xl(2) = -2 * x + 4 * y^2;
end

Use @H instead of defining the function to be integrated as char 'H'. The latter is still working, but outdate for 15 years now.

[baran erbas]

I tried this but it gives error

Index exceeds the number of array elements (1).

Error in batu>H (line 7)

xl(1) = x(2);

Error in odearguments (line 90)

f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in batu (line 2)

[y,x] = ode45(@H, [0,1], [0,1]);

what is the problem???