I'm not sure to which point this is maybe already done by Mathematica. Figure 2: Graph of number of Mathematica functions as a function of time Among the 3000+ functions in Mathematica, there are two major superfunctions that are used to solve differential equations: DSolve and NDSolve. If you do this, you get the form y ( t) f ( y, t) When the right hand side is very complex it might worth to compile it. of functions in Mathematica since its inception back in the late 1980s.
Ndsolve mathematica code#
I would be very glad if anyone could help me here - is there anything wrong with my code? but what could it be, as the code is not exactly rocket science - or at least tell me, if you think my thread was posted to the wrong section. Let me give you a short example: You surely know that you can transform your differential equation into a system of deq of order 1. We present two other options to find a numerical value of a solution to the initial value problem using NDSolve. However, because its results are based on numerical sampling and error.
Ndsolve mathematica how to#
Hrabovsky This article describes how to model diffusion using NDSolve, and then compares that to constructing your own methods using procedural, functional, rule-based, and modular programming. For most differential equations, the results given by NDSolve are quite accurate. The orbits in xy plane should be circular and go "around" the torus (like a satellite).įor comparison, I also plotted the torus in the xy plane, as the orbits should be circular or at least elliptical, and they seem completely wrong - like if there was no torus at all, they cross the planet, which is of course wrong - something like the case shown in attachment, remember, this is the xy plane! Although Mathematica is able to solve this problems explicitly, its solution is represented through a special Bessel function. The Mathematica Journal Diffusion Modeling Programming in Multiple Paradigms George E. NDSolve can also handle differential-algebraic equations that mix differential equations with algebraic ones. X has been chosen close to the toroid (9.5), because the potential is lowest near the toroid.
I need to solve a system of 2nd order differential equations, that look something like No countries or regions match that entry. I am computing orbits of constant energy in a gravitational potential of a complicated planet (sth like a torus).
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