Modules
The library root imports every module below.
| Module | Contents |
|---|---|
NeumannCosine.Basic |
The mode, its frequency, orthogonality and Gram values |
NeumannCosine.Series.TermwiseIntegral |
Termwise integration of $\ell^1$ cosine series |
NeumannCosine.Series.Products |
Products of $\ell^1$ cosine series, interchange with the integral, signed-index reindexing |
NeumannCosine.KernelIntegrals |
Closed forms of integrals of products of three and four modes |
NeumannCosine.ProductIdentities |
Integrals of products of two to four cosine series as constrained convolutions |
NeumannCosine.Coefficients |
The class NeumannW21: $O(k^{-2})$ coefficients, summability, pointwise expansion |
NeumannCosine.Sobolev.WeakDerivative |
Weak derivatives on $(0,L)$, du Bois-Reymond, absolutely continuous representative |
NeumannCosine.Sobolev.H2Neumann |
$H^2(0,L)$ with Neumann trace lies in NeumannW21 |
NeumannCosine.DivergenceFormProjection |
$\lvert\int_0^L(R_0+R_1')\cos(k\pi x/L)\,dx\rvert\le(L+k\pi)B$ when $\lvert R_0\rvert,\lvert R_1\rvert\le B$ on $[0,L]$, $R_0$ is integrable, $R_1$ is absolutely continuous on $[0,L]$ (or continuous on $[0,L]$ and differentiable at every point of $(0,L)$ with integrable derivative), and $R_1(0)=R_1(L)=0$ |
NeumannCosine.Discrete.Eigenvalues |
Discrete and continuum eigenvalues, $\operatorname{sinc}^2$ relation, convergence, lower bound |
NeumannCosine.Discrete.Laplacian |
The reflected three-point stencil on Fin (N + 1), its cosine eigenvectors and basis |
NeumannCosine.Discrete.ModalMinimumTail |
One tail cutoff for all fine meshes, for a linearly coercive $f$ |
NeumannCosine.Discrete.ModalMinimumLimit |
The discrete modal minimum converges to the continuum infimum |