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

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Introduction Properties Pros and Cons Examples References 1st order case: RKC1 Then compare these with the recursive definition of Pj, we get, ˜µ1 = w1 , (34) w0 µj = 2w0 ˜µj = 2w1 bj bj−1 bj , νj = − bj bj−1 Ts(w0)T ′ j cj = (w0) T ′ s(w0)Tj(w0) � j2 /s 2 bj−2 , (35) , ˜γj = 0, (2 � j � s) (36) (37)
Introduction Properties Pros and Cons Examples References 2nd order case: RKC2 T ′′ j (w0) (T ′ j s2 , w1 = T ′ s(w0) T ′′ aj = 1 − bjTj(w0), bj = w0 = 1 + ɛ (w0)) 2 , (2 � j � s) (38) , (39) s (w0) a0 = 1 − b0, a1 = 1 − b1w0, b0 = b1 = b2 (40) β(s) � (w0 + 1)T ′′ s (w0) T ′ � s(w0) 2 3 (s2 − 1)(1 − 2 ɛ), ɛ → 0 (41) 15 From the pictures,we can tell ɛ = 2 13 is a suitable choice.
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Runge Kutta Chebyshev Method for parabolic ... - Brown University

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