# best software package to numerically solve high order nonlinear ODE boundary value problem

I need to numerically solve a 4th and 5th order nonlinear ODE BVP and I was hoping I could get some advice on the best software package to solve these types of problems. I've used MATLABS bvp4c for the 4th order equation and I'm not too confident in the solutions, I am hoping to try another method. Any advice will be helpful! Thanks!

• I don't know about "best", but you could try Maple, which has a variety of solution methods. Is your problem particularly difficult? For example, is it stiff, or singular, or does it have narrow boundary layers? Perhaps you could give us an example of the type of problem you're looking at. – Robert Israel Dec 19 '18 at 18:17
• Could you also quantify or at least qualify how you determine your non-confidence in the BVP solution? Does it change materially when you change the tolerances? Is the ode45 forward solution far away from the bvp4c solution? – LutzL Dec 19 '18 at 18:44
• What do your mean by "order"? The highest order derivative, the highest non-linear term, or higher order methods like RK5(4) and beyond? That would help., – ggcg Dec 19 '18 at 21:00
• Also, are you asking about s/w packages or "methods"? This is a big deal as many "packages" will have all the same methods so what's really the point? MAPLE and Mathematica have pretty good ODE solvers and there is the open source ODEINT. If you are not confident in your answer I would recommend posting some code and letting us check it. You can't make a finite solver of a continuous "work" unless you check outputs and use step size control and other features. MATLAB requires you to check, MAPLE for example uses 1000's of intermediate steps for each step to converge. – ggcg Dec 19 '18 at 21:03
• Are you aware of the existence of "stiff solvers" in Matlab like "ode15s" ? – Jean Marie Dec 19 '18 at 21:13