CppNoddy: include/ODE_EVP.h File Reference

A specification of a class for an $n^{th}$ -order ODE LINEAR EVP defined by. More...

#include <memory>
#include <algorithm>
#include <DenseVector.h>
#include <DenseMatrix.h>
#include <Equation_2matrix.h>
#include <Exceptions.h>
#include <Uncopyable.h>
#include <OneD_Node_Mesh.h>
#include <LinearEigenSystem_base.h>
#include <Residual.h>

Go to the source code of this file.

Classes
class	CppNoddy::ODE_EVP< _Type >
	A templated object for real/complex vector system of first-order ordinary differential equations. More...

Namespaces
namespace	CppNoddy
	A collection of OO numerical routines aimed at simple (typical) applied problems in continuum mechanics.

Detailed Description

A specification of a class for an $n^{th}$ -order ODE LINEAR EVP defined by.

$\lambda M_1({\underline f}(x),x ) \cdot {\underline f } + M_0({\underline f}(x),x ) \cdot {\underline f}^\prime (x) = {\underline R}( {\underline f}(x), x )\,,$

subject to zero Dirichlet conditions defined at $x = x_{left}$ or $x_{right}$ for some components of ${\underline f}(x)$ . The routine constructs a banded 2nd order finite-difference (banded) representation of the EVP in the form

$A_{M\times M} {\underline x} = \lambda B_{M\times M} {\underline x}$

which can then be solved via the LinearEigenSystem class where $M = N \times O$ for an order O equation and N (uniformly spaced) mesh points. The default configuration uses the DenseLinearEigenSystem class for solution via LAPACK although ARPACK can be used if you really know the resulting system has the correct mass matrix properties (typically it wont!).

Definition in file ODE_EVP.h.

Classes

Namespaces

Detailed Description