Runge Kutta Chebyshev Method for parabolic ... - Brown University

Introduction Properties Pros and Cons Examples References
Stability function
Scalar test equation:
Ps is defined recursively:
˙U(t) = λU(t) (20)
Un+1 = Ps(z)Un, z = τλ (21)
P0(z) = 1, (22)
P1(z) = 1 + ˜µ1z, (23)
Pj(z) = (1 − µj − νj) + ˜γjz + (µj + ˜µjz)Pj−1(z) + νjPj−2(z) (2 �
(24)
for each stage, we have
Uj = Pj(z)Un, (0 � j � s) (25)