- #1
Romik
- 14
- 0
Hi all,
I have been stopped by a sextic (6th degree) polynomial in my research. I need to find the biggest positive root for this polynomial symbolically, and since its impassible in general, I came up with this idea, maybe there is a way to approximate this polynomial by a lower degree polynomial which is solvable.
κ2/112 (A2 ) u6+κ2/16 (A2 ) u5+κ2/20 (1/2 B2+3 A2 ) u4+κ2/8 (A2+B2 ) u3-((ω2-B2 κ2)/6) u2+ν2 κ2 ω2=0
this polynomial is come from a nonlinear PDE related to waves.
κ, A, B, v, ω , u are not constant.
I appreciate any helpful comment or solution.
Thanks,
Romik
I have been stopped by a sextic (6th degree) polynomial in my research. I need to find the biggest positive root for this polynomial symbolically, and since its impassible in general, I came up with this idea, maybe there is a way to approximate this polynomial by a lower degree polynomial which is solvable.
κ2/112 (A2 ) u6+κ2/16 (A2 ) u5+κ2/20 (1/2 B2+3 A2 ) u4+κ2/8 (A2+B2 ) u3-((ω2-B2 κ2)/6) u2+ν2 κ2 ω2=0
this polynomial is come from a nonlinear PDE related to waves.
κ, A, B, v, ω , u are not constant.
I appreciate any helpful comment or solution.
Thanks,
Romik