... XI
8 Jump-Adapted Strong Approximations 347
8.1 IntroductiontoJump-AdaptedApproximations 347
8.2 Jump-AdaptedStrongTaylorSchemes 350
8.3 Jump-AdaptedDerivative-Free Strong Schemes 355
8.4 Jump-AdaptedDrift-ImplicitSchemes ... ∈
{1, 2, ,m} . Again, we may, for instance, define the (j, k)-th time trans-
formation by
ϕ
j, k
(t)=
b
2
j, k
2c
j, k
e
2c
j, k
t
− 1
(2.3.26)
for t ∈ [0, ∞), b...
... differential module (M, ∂)(orsimplyM)ofdimensionn is
a k-vector space as dimension n equipped with an additive map ∂ : M → M
which has the property: ∂(fm)=f
m + f m for all f ∈ k and m ∈ M. ✷
A differential ... implies that V
q
has dimension 1
and compare with Remark 3.34. ✷
Exercise 3.36 Semi-simple differential modules over
K.
We recall, see 2.37, that a differential module M...
... Brussels, Belgium
Junkichi Satsuma
University Tokyo, Graduate School
of Mathematical Sciences
Komaba 3-8 -1 , 153 Tokyo, Japan
Pavel Winternitz
C.R.D.E., Universit
´
edeMontreal
H3C 3J7 Montreal, Quebec, ... side. Among the 1 + 1-dimensional integrable equations,
those with one family include KdV, the AKNS, Hirota-Satsuma and Boussi-
nesq equations; they also include the Sawada-Kotera...
... u
j 1,l
∆
2
+
u
j, l+1
− 2u
j, l
+ u
j, l−1
∆
2
= ρ
j, l
(19.0.5)
or equivalently
u
j+ 1,l
+ u
j 1,l
+ u
j, l+1
+ u
j, l−1
− 4u
j, l
=∆
2
ρ
j, l
(19.0.6)
To write this system of linear equations in matrix form we ... Partial Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 2 1-4 310 8-5 )
Copyright (C) 198 8-1 9...
... Partial Differential Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 2 1-4 310 8-5 )
Copyright (C) 198 8-1 992 by Cambridge University Press.Programs Copyright ... Problems
843
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 2 1-4 310 8-5 )
Copyright (C) 198 8-1 992 by Cambridge University Pre...