BVPSOL プログラム構成

code
http://www.zib.de/Numerik/numsoft/CodeLib/codes/bvpsol/

readme より

The distribution contains the following files:

bvpsol.f the solver
bvpsol.nrm output of the example
linalg_bvpsol.f dense linear algebra (deccon,solcon)
ma28_bvpsol.f sparse linear algebra (ma28)
main_bvpsol.f main example program
main_bvpsol.data test data for the example program
makefile makefile for compilation
readme this file
zibconst.f machine dependant constants
zibsec.f machine dependant timing routine

main_bvpsol.f 内で，以下を構成する．

Function FCN : SUBROUTINE F(N, X, Y, D)
- N :（入力）Dimension of the differential equation
- X :（入力）the time (M 個の断面通過時刻は，T(1), T(2), ..., T(M)）
- Y :（入力）状態値
- D :（出力）dY/dt(t=X)

Boundary Condition BC : SUBROUTINE R(YA,YB,W)
- YA :（入力）境界 A(=T(1)) での状態値
- YB :（入力）境界 B(=T(M)) での状態値
- W :（出力）境界条件値

BLFCNI : Computation of the residual vector
needs BC

http://www.uni-bayreuth.de/departments/math/~rbaier/www/doc/elib_description.txt より転載

Program Desciptions of ELib:
============================

Date: 13. 12. 1994

PARANUSS:
This directory contains several subroutines for the parallel
factorization of a real matrix A: the Cholesky decomposition,
the LU- and the QR-factorization. Besides, there are several
auxiliary routines which are used from the factorization
routines.

bespak:
BESPAK is a library of Fortran subroutines for Bessel functions of complex
argument and real (integer or fractional) order.

cmlib:
ODRPACK:
software for weighted orthogonal distance regression
(orthogonal distance regression, nonlinear least squares,
errors in variables)

VFFT:
A vectorized package of Fortran subprograms for the
fast Fourier transform of multiple real periodic sequences

VHS3:
A VECTORIZED PACKAGE OF FORTRAN SUBPROGRAMS FOR THE SOLUTION
OF A THREE-DIMENSIONAL HELMHOLTZ EQUATION ON A STAGGERED GRID

VSFFT:
A VECTORIZED PACKAGE OF FORTRAN SUBPROGRAMS FOR THE FAST
TRANSFORM OF MULTIPLE REAL SEQUENCES DEFINED ON A STAGGERED GRID

XERROR:
A package of Fortran subprograms for the processing of error
messages. It is used by many of the prewritten library
subroutines in CMLIB.

codelib:
etliche Subdirs
alcon1:
(Al)gebraic system of equations (Con)tinuation method.

Written by P. Deuflhard, P. Kunkel
Purpose Solution of parameter dependent systems of
nonlinear equations.
Method Numerical pathfollowing with automatic steplength
control
Category F4 - Parameter Dependent Nonlinear Equation
Systems
Keywords Numerical pathfollowing, Homotopy Method

alcon2:
vgl. alcon1

bvplsq:
(B)oundary (V)alue (P)roblem (L)east (Sq)uares Solver for highly
nonlinear (possibly overdetermined) two point boundary value
problems.

Written by P. Deuflhard, G.Bader
Purpose Solution of overdetermined nonlinear two-point
boundary value problems.
Method Local Nonlinear two-point Boundary Value
least squares problems solver
(Multiple shooting approach)
Category I1b2a - Differential and integral equations
Two point boundary value problems
Keywords Nonlinear boundary value problems, Multiple
shooting, Gauss Newton methods

bvpsog:
(B)oundary (V)alue (P)roblem (So)lver for highly nonlinear
two point boundary value problems using a (G)lobal sparse linear
solver for the solution of the arising linear subproblems.

Written by P. Deuflhard, G.Bader, L. Weimann
Purpose Solution of nonlinear two-point boundary value
problems.
Method Global Nonlinear two-point Boundary Value
Problems solver (Multiple shooting approach)
Category I1b2a - Differential and integral equations
Two point boundary value problems
Keywords Nonlinear boundary value problems, Multiple
shooting, Newton methods

bvpsol:
(B)oundary (V)alue (P)roblem (So)lver for highly nonlinear
two point boundary value problems using a (L)ocal linear
solver (condensing algorithm) for the solution of the arising
linear subproblems.

Written by P. Deuflhard, G.Bader, L. Weimann
Purpose Solution of nonlinear two-point boundary value
problems.
Method Local Nonlinear two-point Boundary Value
Problems solver (Multiple shooting approach)
Category I1b2a - Differential and integral equations
Two point boundary value problems
Keywords Nonlinear boundary value problems, Multiple
shooting, Newton methods

difex1:
Explicit extrapolation integrator for non-stiff systems of
ordinary first-order differential equations.

ritten by P. Deuflhard, U. Nowak, U. Poehle
urpose Solution of systems of initial value problems
ethod Explicit mid-point rule discretization with
h**2-extrapolation
ategory i1a1c1. - System of nonstiff first order
differential equations
eywords extrapolation, ODE, explicit mid-point rule,
nonstiff
difex2:
Explicit extrapolation integrator for non-stiff systems of
second-order differential equations with the first derivative
absent in the right-hand side (based on Stoermer discretization).

Special version adapted for possible call in the multiple shooting
code BVPSOL.

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Explicit mid-point rule discretization with
h**2-extrapolation
Category i1a1c2. - System of nonstiff second order
differential equations
Keywords extrapolation, ODE, explicit mid-point rule,
non-stiff

difexm:
Explicit extrapolation integrator for non-stiff systems of
second-order differential equations with the first derivative
present in the right-hand side FCN of the special form:

f(t,y(t)) + L(t,y(t)) * y'(t) , L : diagonal matrix

(based on modified Stoermer discretization).

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Explicit mid-point rule discretization with
h**2-extrapolation
Category i1a1c1. - System of nonstiff first order
differential equations
Keywords extrapolation, ODE, explicit mid-point rule,
nonstiff

eulex:
Explicit extrapolation integrator for non-stiff systems of
ordinary first-order differential equations.

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Explicit Euler discretization with
h-extrapolation
Category i1a1c1. - System of nonstiff first order
differential equations
Keywords extrapolation, ODE, explicit Euler, nonstiff

eulsim:
Integrator for stiff systems of ordinary differential equations.

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Semi-implicit Euler discretization with
h-extrapolation
Category i1a2a. - System of stiff first order differential
equations
Keywords extrapolation, ODE, semi-implicit Euler, stiff

gbit1:
Good Broyden package with user interface and test example
Iterative solution of a linear system (implicitly given matrix
by subroutine MULJAC - computes A*vector)

Written by U. Nowak, L. Weimann
Purpose Iterative solution of large scale systems of
linear equations
Method Secant method Good Broyden with adapted
linesearch
Category D2a. - Large Systems of Linear Equations
Keywords Linear Equations; Large Systems;
Iterative Methods

giant:
Numerical solution of large scale highly nonlinear systems with
Global (G) Inexact (I) Affine-invariant (A) Newton (N)
Techniques (T)

Written by U. Nowak, L. Weimann
Purpose Solution of large scale systems of highly
nonlinear equations
Method Damped affine invariant Newton method combined
with iterative solution of arising linear systems
(see references below)
Category F2a. - Systems of nonlinear equations
Keywords Nonlinear equations, large systems,
inexact Newton methods, iterative methods

kaskade:
family of adaptive finite element methods
finite element methods in 2 and 3 space dimensions
modular procedures, you can incorporate your own procedures for
triangulations, direct/iterative solvers, estimator methods,
implemented applications:
ELLKASK 2D: linear, scalar, second-order, elliptic equation in
2 dimensions
ELLKASK 3D: same in 3 dimensions
KASTIO: parabolic equation in 2 space dimensions
KARDOS: semilinear, parabolic initial boundary value problems in
one dimension
drawing routines

keplex:
Explicit extrapolation integrator for non-stiff second-order
systems of ordinary differential equations of the form

y" + (om**2) * y = f(t,y) ,
om : given fixed frequency

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Kepler discretization with h**2-extrapolation
Category i1a1c2. - System of nonstiff second order
differential equations
Keywords extrapolation, ODE, Kepler discretization,
nonstiff

larkin_3.1:
P. DEUFLHARD, G. BADER, U. NOWAK: *
LARKIN - A SOFTWARE PACKAGE FOR THE SIMULATION OF LARGE *
SYSTEMS ARISING IN CHEMICAL REACTION KINETICS *
(UNIV. HEIDELBERG, SFB 123: TECHN. REP. 100 (1980)) *
IN: *
K.H. EBERT, P. DEUFLHARD, W. JAEGER (ED.): *
MODELLING OF CHEMICAL REACTION SYSTEMS. *
SPRINGER SERIES CHEM. PHYS. 18 (1981) *

limex:
Numerical solution of Linearly IMplicit differential-algebraic
systems with EXtrapolation techniques

Written by U. Nowak, J. Zugck
Purpose Solution of linearly implicit differential-
algebraic systems up to index 1.
Method Extrapolation integrator with order and stepsize
control.
(see references below)
Category i1a2b: Stiff and mixed implicit differential-
algebraic systems up to index 1.
Keywords Differential equations, differential-algebraic
systems, extrapolation integrator

limexs:
Numerical solution of Linearly IMplicit differential-algebraic
systems with EXtrapolation and Sparse linear algebra techniques

Written by U. Nowak, J. Zugck
Purpose Solution of linearly implicit differential-
algebraic systems up to index 1.
Method Extrapolation integrator with order and stepsize
control. Sparse matrix techniques for linear
systems
(see references below)
Category i1a2b: Stiff and mixed implicit differential-
algebraic systems up to index 1.
Keywords Differential equations, differential-algebraic
systems, extrapolation integrator, sparse matrix
techniques

metan1:
Integrator for stiff systems of autonomous ordinary differential
equations.

Written by P. Deuflhard, U. Nowak, U. Poehle
Purpose Solution of systems of initial value problems
Method Semi-implicit mid-point rule with
h**2-extrapolation
Category i1a2a. - System of stiff first order differential
equations
Keywords extrapolation, ODE, mid-point rule, stiff

mexx:
MEXX - Numerical Software for the Integration of Constrained
Mechanical Multibody Systems

MEXX (short for MEXanical systems eXtrapolation integrator) is a
Fortran code for time integration of constrained mechanical systems.

Numerical integration of the equations of motion of a
constrained mechanical system, including dry friction
and external dynamics

Written by Ch. Engstler, Ch. Lubich, U. Nowak, U. Poehle
Purpose Solution of the equations of motion of a
constrained mechanical system
Category i1a2c. - Stiff and mixed algebraic-differential
equations, Special Applications
Keywords extrapolation, ODE, constrained mechanical system

mulcon:
(Mul)tiple shooting for parameter dependent two-point boundary
value problems with (Con)tinuation method.

Written by P. Deuflhard, P. Kunkel
Purpose Solution of parameter dependent two-point boundary
value problems.
Method Numerical pathfollowing with automatic steplength
control
Category I1b2b - Differential and integral equations
Parameter-dependent general BVP's
Keywords Numerical pathfollowing, Homotopy Method,
Nonlinear boundary value problems,
Multiple shooting

nleq1:
Numerical solution of nonlinear (NL) equations (EQ)
especially designed for numerically sensitive problems.

Written by U. Nowak, L. Weimann
Purpose Solution of systems of highly nonlinear equations
Method Damped affine invariant Newton method
(see references below)
Category F2a. - Systems of nonlinear equations
Keywords Nonlinear equations, Newton methods

nleq1s:
Numerical solution of systems of nonlinear (NL) equations (EQ)
with a sparse (S) Jacobian -
especially designed for numerically sensitive problems.

Written by U. Nowak, L. Weimann
Purpose Solution of systems of highly nonlinear equations
with a sparse Jacobian matrix
Method Damped affine invariant Newton method
(see references below)
Category F2a. - Systems of nonlinear equations
Keywords Nonlinear equations, Newton methods,
sparse Jacobian

nleq2:
Numerical solution of nonlinear (NL) equations (EQ)
especially designed for numerically sensitive problems.

Written by U. Nowak, L. Weimann
Purpose Solution of systems of highly nonlinear equations
Method Damped affine invariant Newton method with rank-
strategy (see references below)
Category F2a. - Systems of nonlinear equations
Keywords Nonlinear equations, Newton methods

nlscon:
Numerical solution of nonlinear (NL) least squares (S)
problems with nonlinear constraints (CON), especially
designed for numerically sensitive problems.

Written by U. Nowak, L. Weimann
Purpose Solution of highly nonlinear, optionally
constrained least squares problems
Method Damped affine invariant Gauss-Newton method
(see references below)
Category K1b2b. - Nonlinear least squares approxi-
mation with nonlinear constraints
Keywords Nonlinear least squares problems,
Gauss-Newton methods

perhom:
(Per)iodic Solution of Nonlinear One-Parameter-Dependent Ordinary
Differential Equations using (Hom)otopy Method.

Written by P. Deuflhard, R. Winzen
Purpose Solution of nonlinear parameter dependent
two-point boundary value problems with period
solutions of an unknown period length
Method Local Nonlinear two-point Boundary Value
Problems solver (Multiple shooting approach),
Homotopy Method
Category I1b2b - Differential and integral equations
Parameter-dependent general BVP's
Keywords Nonlinear boundary value problems, Multiple
shooting, Newton methods, Period solutions,
Homotopy

period:
(Period)ic Solution of Nonlinear Ordinary Differential Equations

Written by P. Deuflhard, R. Winzen
Purpose Solution of nonlinear two-point boundary value
problems with period solutions of an unknown
period length
Method Local Nonlinear two-point Boundary Value
Problems solver (Multiple shooting approach)
Category I1b3 - Differential and integral equations
Eigenvalue problems
Keywords Nonlinear boundary value problems, Multiple
shooting, Newton methods, Period solutions

symcon:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% SYMCON %%
%% hybrid algorithm of mixed symbolic numerical type %%
%% for the treatment of parameter dependent systems %%
%% of equations F(x,l) = 0 %%
%% (use of the theory of linear representations, %%
%% pathfollowing algorithm, computation of %%
%% bifurcation methods) %%
%% Authors: Dr. K. Gatermann (symbolic part) %%
%% A. Hohmann (numerical part) %%
%% 24. 7. 1991 %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

dhlib:
Die folgende Beschreibung gibt einen Ueberblick ueber die
zugaenglichen Algorithmen aus dem Buch

Numerische Mathematik
Eine algorithmisch orientierte Einfuehrung,

von P. Deuflhard und A. Hohmann,

erschienen bei Walter de Gruyter, Berlin, 1991

1. Lineare Gleichungssyteme
2. Fehleranalyse
3. Lineare Ausgleichsprobleme
4. Nichtlineare Gleichungssysteme und Ausgleichsprobleme
5. Symmetrische Eigenwertprobleme
6. Drei-Term-Rekursionen
7. Interpolation und Approximation
8. Grosse symmetrische Gleichungssyteme und Eigenwertprobleme
9. Bestimmte Intergrale

hairer-wanner:
codes of the books "Solving ODEs I and II" of Prof. Hairer and Prof. Wanner

nonstiff differential equations
-------------------------------
Dormand-Prince 5(4) with dense output of order 4
Dormand-Prince 8(5,3) with dense output of order 7
Extrapolation method with dense output
Dormand-Prince 5(4) for delay differential equations

stiff differential equations and DAEs
-------------------------------------
implicit Runge-Kutta method of order 5 (Radau IIA)
for My'=f(x,y) with possibly singular matrix M with dense output
(collocation method)
diagonally-implicit Runge-Kutta method of order 4
for My'=f(x,y) with possibly singular matrix M with dense output
algebraic order conditions are considere
Classical Rosenbrock methods of order 4(3)
for My'=f(x,y) with possibly singular matrix M with dense output
algebraic order conditions are considere
Extrapolation method based on linearly implicit Euler
for My'=f(x,y) with possibly singular matrix M with dense output
Extrapolation method based on linearly implicit mid-point rule
for My'=f(x,y)

mechanical systems
------------------
code specially adapted to the equations of motion
for constrained mechanical systems:
q' = T(q,t)v
M(t,q)v' = f(q,v,u,t) - L(q,v,u,t)*lamda
0 = H(q,t)v + k(q,t)
u' = d(q,v,u,lambda,t)
it has the option of projecting the numerical solution to manifolds
defined by 0 = g(q,t). A dense output is available.

nms:
keine Dokumentation!

pcon60:
PCON60 is a program which produces successive solutions y of a system of
nonlinear equations with one degree of freedom. The program can be used to
study parameterized problems, structures under a varying load, or the
equilibrium curve of a physical system. See TRACE for a related, but
much simplified program for solving a single equation F(X,Y)=0.

specfn:
SPECFN is a library of double precision Fortran subroutines for error and
complementary error functions, exponential and scaled exponential integrals,
sine and cosine integrals, and hyperbolic sine and cosine integrals. The
software assumes a floating-point mantissa length of 60 bits and an
overflow limit of approximately 10^308 but these values can be changed
by altering DATA statements. The methods used are power series, continued
fractions, and asymptotic series.

systolic:
Solution of Quadrature Problems on Finite Intervals
Using Trapeziodal Sums with Polynomial Extrapolation.
Implemented for Transputer based systems
running under TDS (Transputer Development System).

Explicit extrapolation integrator for
non-stiff systems of ordinary differential
equations. Based on explicit Euler discretization.
Implemented for Transputer based systems
running under TDS (Transputer Development System)

Semi-implicite extrapolation integrator for
stiff systems of ordinary differential equations.
Implemented for Transputer based systems running
under TDS (Transputer Development System)

test:
Test implementations