MATLAB: Ode23 and ode45 problem

ode23 ode45

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?

Best Answer

% 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

Related Solutions

MATLAB: Solving second order ODE with ode45

Since you start at x=0, you divide by zero in the line

dy_le_dx(2)=(1/x)*(x*y(2)-(x^2-n^2));

Best wishes

Torsten.

MATLAB: I want to add

Based on your comment on other question for expression of ea(t): https://www.mathworks.com/matlabcentral/answers/541922-please-tell-me-how-to-use-ode45-code#comment_883106 the following shows how to use ode45 to solve this ODE with input saturation

[t, y] = ode45(@odeFun, [0 1], [0; 0]);
plot(t, y(:,1), 'o-')
function dxdt = odeFun(t, x)
    % transfer function is equivalent to following ODE
    % x'' = 4/9(-16x'+ea(t))
    ea = (1-x(1))*303;
    if ea > 100
        ea = 100;
    elseif ea < -100
        ea = -100;
    end
    dxdt = zeros(2, 1);
    dxdt(1) = x(2);
    dxdt(2) = 4/9*(-16*x(2)+ea);
end

Best Answer

Related Solutions

MATLAB: Solving second order ODE with ode45

MATLAB: I want to add

Related Question