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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?

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John D'Errico
John D'Errico 2019-5-26
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
baran erbas 2019-5-26
Because i have no idea about this question if you can give me an example solution i will try to solve my question.

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Stephan
Stephan 2019-5-26

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% 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

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baran erbas
baran erbas 2019-5-26
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
Jan 2019-5-27
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
baran erbas 2019-5-27
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???

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