The main role is played by the second order
linear differential equation which these polynomials satisfy since this yields the electrostatic interpretation.
Let us consider the first order
linear differential equation for [??],
[17] Horng-Jaan Li and Cheh-Chih Yeh, On the nonoscillatory behavior of solutions of a second order
linear differential equation, Math.
Third-Order
Linear Differential Equation with Oscillating and Nonoscillating Solutions
Sun, "Hyers-Ulam stability of
linear differential equations of first order," Applied Mathematics Letters, vol.
First of all, we consider the complex dynamical properties of solutions to second order
linear differential equations with polynomial coefficients and obtain the following two remarks.
Xu, "Hyers-Ulam stability of a class of fractional
linear differential equations," Kodai Mathematical Journal, vol.
To overcome this problem, an analytical approach is used, which converts the original nonlinear differential equation to a
linear differential equation, that can be solved in closed form at each time step [14].
As noted above, in Section 5.1 we determine a particular solution of a non-homogeneous
linear differential equation with piecewise constant coefficients and piecewise continuous right side.
This is easy to verify by solving or simulating the
linear differential equation (3c) relative to [M.sub.B](t).
which is theso-called areolar
linear differential equation [9, pp.