initial values

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11—20 of 26 matching pages

11: 15.19 Methods of Computation

… ►Initial values for moderate values of

|a|

and

|b|

can be obtained by the methods of §15.19(i), and for large values of

|a|

|b|

, or

|c|

via the asymptotic expansions of §§15.12(ii) and 15.12(iii). …

12: 9.12 Scorer Functions

… ►

§9.12(iii) Initial Values

…

13: Bibliography T

… ►

J. G. Taylor (1978) Error bounds for the Liouville-Green approximation to initial-value problems. Z. Angew. Math. Mech. 58 (12), pp. 529–537.

ⓘ

External Links:: ISSN 0044-2267, Document, MathReview, ZentralBlatt
Referenced by:: §2.7(iii).
Encodings:: BibTeX

…

14: 18.9 Recurrence Relations and Derivatives

… ►with initial values

p_{0}(x)=1

and

p_{1}(x)=A_{0}x+B_{0}

. … ►with initial values

p_{0}(x)=1

and

p_{1}(x)=a_{0}^{-1}(x-b_{0})

. …

15: 3.6 Linear Difference Equations

… ►We first compute, by forward recurrence, the solution

p_{n}

of the homogeneous equation (3.6.3) with initial values

p_{0}=0

p_{1}=1

. …

16: 3.8 Nonlinear Equations

… ►From this graph we estimate an initial value

x_{0}=4.65

. …

17: 3.11 Approximation Techniques

… ►with initial values

T_{0}\left(x\right)=1

T_{1}\left(x\right)=x

. …

18: 18.5 Explicit Representations

…

19: 28.2 Definitions and Basic Properties

… ►Furthermore, a solution

w

with given initial constant values of

w

and

w^{\prime}

at a point

z_{0}

is an entire function of the three variables

z

a

, and

q

. …

20: 32.11 Asymptotic Approximations for Real Variables

… ►Next, for given initial conditions

w(0)=0

and

w^{\prime}(0)=k

, with

k

real,

w(x)

has at least one pole on the real axis. There are two special values of

k

k_{1}

and

k_{2}

, with the properties

-0.45142\;8<k_{1}<-0.45142\;7

1.85185\;3<k_{2}<1.85185\;5

, and such that: …