Questions about bvp4c solution

Hi, I solved correctly a system of ODE second order with BCs, with the instruction bvp4c.

However, I have some questions about it.

My code is as follows:

...
xmesh = linspace(1e-5,1.5*1e-3,20);      
solinit = bvpinit(xmesh,1e-3*[0,0,0,0,1,1,1,1]);
sol = bvp4c(@bvpfcn,@bcs,solinit);
plot(sol.x,sol.y)

1) When I plot the solution, I should choose in x interval sol.x or xmesh? What is their difference?

2) I don't understand how Matlab uses the second vector [0,0,0,0,1,1,1,1] in bvpinit.

It should represent the initial guess of solution (I have 8 variables), but it seems that its values don't change final solution. Is it right?

I've already read Matlab guide about bvp4c, but I have not found these answers.

Thank you!

Answer 1

[Shadaab Siddiqie]

From my understanding you have few doutes on the arguments of bvp4c function.

1. 'bvp4c' function not output 'sol.stats' when 'NMax' is exceeded, This is a due to what the 'stats' object returns. Typically, it has values that are associated with a solved problem, rather than an incomplete one.
2. solinit are the Initial guess of solution, specified as a structure. Use bvpinit to create solinit. Unlike initial value problems, a boundary value problem can have no solution, a finite number of solutions, or infinitely many solutions. An important part of the process of solving a BVP is providing a guess for the required solution. The quality of this guess can be critical for the solver performance and even for a successful computation. For some guidelines on creating a good initial guess, see Initial Guess of Solution. But it is not nessary for the solution to change if the initial conditions are changed.

[Elia Paini]

Ok, thank you!