Finds a numerical solution
to an ODE of order n, by the 4.th order Runge-Kutta method.
The order of the ODE, n, is obtained from the (same)
number of initial values. The problem solved is
t² y" − 2 t y' +
2 y = t³ lnt or
y" = 2 y' ⁄ t
− 2 y ⁄ t²
+ t lnt
As given above, the initial values are y(1) = 1
and y'(1) = 0; and the parameters are those shown
in the formula.
For the base problem, the analytical solution is:
y = (7⁄4)t + (1⁄2 lnt
− 3⁄4) t³
Plots, vs. time:
(i) x (function), left-h. y-axis;
(ii) x' (derivative), right-h. y-axis; and
(iii) the analytical solution, left-h. y-axis.
Reported x(2) is 0.272588 .
Other suggested data:
tfinal = 2.5. |
• Zworski,
Maciej, Burden &
Faires.pdf, Probl. 2
• Sher, Miller, Jacobovits, Soyk, Medina, ODE_NYU_EqToSys.pdf, 1 p
(N. Y. Univ.).
• Tseng, Zack, ODE_PSU_Tseng_EqToSys.pdf,
40 pp (Penn State).
• Rutgers U., ODE_Rutgers_BiomEng_Ch7.pdf, 98 pp.
• Mørken, Knut Martin, ODE_UOslo_kap13.pdf, 46 pp
(U. Oslo).
• 1934-04-06: Ostrovskii, Iossif Vladimirovich
(–). |
