boundary conditions

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1—10 of 22 matching pages

1: 32.5 Integral Equations

… ►satisfies

\mbox{P}_{\mbox{\scriptsize II}}

with

\alpha=0

and the boundary condition …

2: 20.13 Physical Applications

… ►These two apparently different solutions differ only in their normalization and boundary conditions. …Theta-function solutions to the heat diffusion equation with simple boundary conditions are discussed in Lawden (1989, pp. 1–3), and with more general boundary conditions in Körner (1989, pp. 274–281). …

3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►

Self-adjoint extensions of (1.18.28) and the Weyl alternative

… ► A boundary value for the end point

a

is a linear form

\mathcal{B}

\mathcal{D}({\mathcal{L}}^{*})

of the form …Then, if the linear form

\mathcal{B}

is nonzero, the condition

\mathcal{B}(f)=0

is called a boundary condition at

a

. Boundary values and boundary conditions for the end point

b

are defined in a similar way. … ►The above results, especially the discussions of deficiency indices and limit point and limit circle boundary conditions, lay the basis for further applications. …

4: 32.14 Combinatorics

… ►and

w(x)

satisfies

\mbox{P}_{\mbox{\scriptsize II}}

with

\alpha=0

and boundary conditions …

5: 10.73 Physical Applications

… ►and on separation of variables we obtain solutions of the form

e^{\pm in\phi}e^{\pm\kappa z}J_{n}\left(\kappa r\right)

, from which a solution satisfying prescribed boundary conditions may be constructed. … ►With the spherical harmonic

Y_{\ell,m}\left(\theta,\phi\right)

defined as in §14.30(i), the solutions are of the form

f=g_{\ell}(k\rho)Y_{\ell,m}\left(\theta,\phi\right)

with

g_{\ell}=\mathsf{j}_{\ell}

\mathsf{y}_{\ell}

{\mathsf{h}^{(1)}_{\ell}}

, or

{\mathsf{h}^{(2)}_{\ell}}

, depending on the boundary conditions. …

6: 1.13 Differential Equations

… ►Assuming that

u(x)

satisfies un-mixed boundary conditions of the form …or periodic boundary conditions … ►For a regular Sturm-Liouville system, equations (1.13.26) and (1.13.29) have: (i) identical eigenvalues,

\lambda

; (ii) the corresponding (real) eigenfunctions,

u(x)

and

w(t)

, have the same number of zeros, also called nodes, for

t\in(0,c)

as for

x\in(a,b)

; (iii) the eigenfunctions also satisfy the same type of boundary conditions, un-mixed or periodic, for both forms at the corresponding boundary points. …