SECTION I. User-callable Routines Category I. Differential and integral equations

```         I1.  Ordinary differential equations
I2.  Partial differential equations

I1.  Ordinary differential equations
I1A.  Initial value problems
I1A1.  General, nonstiff or mildly stiff
I1A1A.  One-step methods (e.g., Runge-Kutta)

DERKF-S   Solve an initial value problem in ordinary differential
DDERKF-D  equations using a Runge-Kutta-Fehlberg scheme.

I1A1B.  Multistep methods (e.g., Adams' predictor-corrector)

DEABM-S   Solve an initial value problem in ordinary differential
DDEABM-D  equations using an Adams-Bashforth method.

SDRIV1-S  The function of SDRIV1 is to solve N (200 or fewer)
DDRIV1-D  ordinary differential equations of the form
CDRIV1-C  dY(I)/dT = F(Y(I),T), given the initial conditions
Y(I) = YI.  SDRIV1 uses single precision arithmetic.

SDRIV2-S  The function of SDRIV2 is to solve N ordinary differential
DDRIV2-D  equations of the form dY(I)/dT = F(Y(I),T), given the
CDRIV2-C  initial conditions Y(I) = YI.  The program has options to
allow the solution of both stiff and non-stiff differential
equations.  SDRIV2 uses single precision arithmetic.

SDRIV3-S  The function of SDRIV3 is to solve N ordinary differential
DDRIV3-D  equations of the form dY(I)/dT = F(Y(I),T), given the
CDRIV3-C  initial conditions Y(I) = YI.  The program has options to
allow the solution of both stiff and non-stiff differential
equations.  Other important options are available.  SDRIV3
uses single precision arithmetic.

SINTRP-S  Approximate the solution at XOUT by evaluating the
DINTP-D   polynomial computed in STEPS at XOUT.  Must be used in
conjunction with STEPS.

STEPS-S   Integrate a system of first order ordinary differential
DSTEPS-D  equations one step.

I1A2.  Stiff and mixed algebraic-differential equations

DEBDF-S   Solve an initial value problem in ordinary differential
DDEBDF-D  equations using backward differentiation formulas.  It is
intended primarily for stiff problems.

SDASSL-S  This code solves a system of differential/algebraic
DDASSL-D  equations of the form G(T,Y,YPRIME) = 0.

SDRIV1-S  The function of SDRIV1 is to solve N (200 or fewer)
DDRIV1-D  ordinary differential equations of the form
CDRIV1-C  dY(I)/dT = F(Y(I),T), given the initial conditions
Y(I) = YI.  SDRIV1 uses single precision arithmetic.

SDRIV2-S  The function of SDRIV2 is to solve N ordinary differential
DDRIV2-D  equations of the form dY(I)/dT = F(Y(I),T), given the
CDRIV2-C  initial conditions Y(I) = YI.  The program has options to
allow the solution of both stiff and non-stiff differential
equations.  SDRIV2 uses single precision arithmetic.

SDRIV3-S  The function of SDRIV3 is to solve N ordinary differential
DDRIV3-D  equations of the form dY(I)/dT = F(Y(I),T), given the
CDRIV3-C  initial conditions Y(I) = YI.  The program has options to
allow the solution of both stiff and non-stiff differential
equations.  Other important options are available.  SDRIV3
uses single precision arithmetic.

I1B.  Multipoint boundary value problems
I1B1.  Linear

BVSUP-S   Solve a linear two-point boundary value problem using
DBVSUP-D  superposition coupled with an orthonormalization procedure
and a variable-step integration scheme.

I2.  Partial differential equations
I2B.  Elliptic boundary value problems
I2B1.  Linear
I2B1A.  Second order
I2B1A1.  Poisson (Laplace) or Helmholz equation
I2B1A1A.  Rectangular domain (or topologically rectangular in the coordinate
system)

HSTCRT-S  Solve the standard five-point finite difference
approximation on a staggered grid to the Helmholtz equation
in Cartesian coordinates.

HSTCSP-S  Solve the standard five-point finite difference
approximation on a staggered grid to the modified Helmholtz
equation in spherical coordinates assuming axisymmetry
(no dependence on longitude).

HSTCYL-S  Solve the standard five-point finite difference
approximation on a staggered grid to the modified
Helmholtz equation in cylindrical coordinates.

HSTPLR-S  Solve the standard five-point finite difference
approximation on a staggered grid to the Helmholtz equation
in polar coordinates.

HSTSSP-S  Solve the standard five-point finite difference
approximation on a staggered grid to the Helmholtz
equation in spherical coordinates and on the surface of
the unit sphere (radius of 1).

HW3CRT-S  Solve the standard seven-point finite difference
approximation to the Helmholtz equation in Cartesian
coordinates.

HWSCRT-S  Solves the standard five-point finite difference
approximation to the Helmholtz equation in Cartesian
coordinates.

HWSCSP-S  Solve a finite difference approximation to the modified
Helmholtz equation in spherical coordinates assuming
axisymmetry  (no dependence on longitude).

HWSCYL-S  Solve a standard finite difference approximation
to the Helmholtz equation in cylindrical coordinates.

HWSPLR-S  Solve a finite difference approximation to the Helmholtz
equation in polar coordinates.

HWSSSP-S  Solve a finite difference approximation to the Helmholtz
equation in spherical coordinates and on the surface of the

I2B1A2.  Other separable problems

SEPELI-S  Discretize and solve a second and, optionally, a fourth
order finite difference approximation on a uniform grid to
the general separable elliptic partial differential
equation on a rectangle with any combination of periodic or
mixed boundary conditions.

SEPX4-S   Solve for either the second or fourth order finite
difference approximation to the solution of a separable
elliptic partial differential equation on a rectangle.
Any combination of periodic or mixed boundary conditions is
allowed.

I2B4.  Service routines
I2B4B.  Solution of discretized elliptic equations

BLKTRI-S  Solve a block tridiagonal system of linear equations
CBLKTR-C  (usually resulting from the discretization of separable
two-dimensional elliptic equations).

GENBUN-S  Solve by a cyclic reduction algorithm the linear system
CMGNBN-C  of equations that results from a finite difference
approximation to certain 2-d elliptic PDE's on a centered
grid .

POIS3D-S  Solve a three-dimensional block tridiagonal linear system
which arises from a finite difference approximation to a
three-dimensional Poisson equation using the Fourier
transform package FFTPAK written by Paul Swarztrauber.

POISTG-S  Solve a block tridiagonal system of linear equations
that results from a staggered grid finite difference
approximation to 2-D elliptic PDE's.

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