How to solve and graph a second order nonlinear differential equation?

Hi everyone,

I'm pretty new to matlab, and have been trying to use bvp4c and ode45 functions to try to solve and graph a second order non linear differential equation, but I'm not sure these are the right ones to use or where I'm going wrong with them. I think the main issue is that, with the bvp4c function, it may require boundary conditions at two locations to be = 0, while my graph should look more like a logarithmic graph.

My equation takes the following form:

y'' + f(y)y' = g(y)

Over the interval 0 < x < 10, with y(10) = A, where A is a constant. Any advice on the right approach to take would be appreciated!

[Torsten]

You need two boundary conditions to solve your equation.

If you impose both conditions at the same end of the integration interval, use ode45or ode15s.

If you impose the two conditions at both ends of the integration interval, use bvp4c.

Answer 1

[Sam Chak]

Hi @Parcher

Not exactly sure what you are tring to solve, but this worth a try, although it may not be the exact solution that you are seeking. However, if is known and is the manipulated variable, then we can design

.

In the following example, is assumed as a bounded nonlinear function, where as well.

% Desired output at y(10)
A = 1

% ODE
f = @(t, x) [x(2); ...
	sin(x(1))*x(2) - 2*x(2) - (x(1) - A) - sin(x(1))*x(2)];

init = [0 0];	% initial condition

tspan = [0 10];

[t, x] = ode45(f, tspan, init);

plot(t, x(:,1))
x(end,1)

Try plotting the output and see if that is desired. You can change the initial value and desired output for A as well.

Answer 2

[Nour]

% Desired output at y(10) A = 1

% ODE f = @(t, x) [x(2); ... sin(x(1))*x(2) - 2*x(2) - (x(1) - A) - sin(x(1))*x(2)];

init = [0 0]; % initial condition

tspan = [0 10];

[t, x] = ode45(f, tspan, init);

plot(t, x(:,1)) x(end,1)