The (n+1)-dimensional Harmonic Oscillator

The (n+1)-dimensional harmonic oscillator equation is of the form:

i$$\phi_{t}^{}$$ = $$\nabla^{2}_{}$$$$\phi$$ + a(x₁² + x₂² + ... + x_n²)$$\phi$$

Before generating the system, we transform t $\mapsto$ it, so the equation has no complex coefficients, and can be more easily dealt with.

The determining systems for this PDE are slightly more complex than the systems for the Laplace equation, as the independent variables occur explicitly in the determining systems, and there is an unknown constant a.

The determining systems consists of equations the dependent variables $\Phi$, T and X01, X02,..., Xn which depend on the independent variables $\phi$, t and x01, x02,..., xn. There is also the constant a.

The systems for n = 3..16 can be downloaded here (the files in the archive are named harosc_n).

For the benchmark, the additional assumption was made that a $\not=$ 0, which is present in the N list for the systems.

	Input		PureElim
Dimension	Equations	Length	Time (sec)	Mem (MB)
3	47	5200	0.01	0.72
4	75	8819	0.04	0.73
5	109	13620	0.06	0.76
6	149	19747	0.10	0.80
7	195	27344	0.17	0.90
8	247	36555	0.32	0.98
9	305	47524	0.48	1.03
10	369	60395	0.71	1.11
11	439	75312	1.01	1.22
12	515	92419	1.77	1.82
13	597	111860	2.53	2.06
14	685	133779	3.89	2.16
15	779	158320	6.63	2.56
16	879	185627	10.45	2.63