COLNEW
Boundary Value Problem Solver Using Collocation

COLNEW is a FORTRAN77 library which solves a mixed-order system of ordinary differential equations (ODE's) subject to separated, multipoint boundary conditions, using collocation at Gaussian points, by Uri Ascher and Georg Bader.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

COLNEW is available in a FORTRAN77 version.

Related Data and Programs:

BVPSOL, a FORTRAN77 library which solves highly nonlinear two point boundary value problems using a local linear solver (condensing algorithm) or a global sparse linear solver for the solution of the arising linear subproblems, by Peter Deuflhard, Georg Bader, Weimann.

FD1D_BVP, a FORTRAN77 program which applies the finite difference method to a two point boundary value problem in one spatial dimension.

FEM1D_BVP_LINEAR, a FORTRAN77 program which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension, and compares the computed and exact solutions with the L2 and seminorm errors.

MUS, a FORTRAN77 library which implements the multiple shooting method for two point boundary value problems, for linear or nonlinear cases, by Robert Mattheij and G Staarink.

Author:

Uri Ascher, Georg Bader

Reference:

1. Uri Ascher, Robert Mattheij, Robert Russell,
   Numerical Solution of Boundary Value Problems for Ordinary Differential Equations,
   Prentice Hall, 1988,
   ISBN: 0-13-627266-5,
   LC: QA379.A83.

Source Code:

• colnew.f, the source code.
• colnew.sh, BASH commands to compile the source code.

Examples and Tests:

• colnew_prb.f, a sample calling program.
• colnew_prb.sh, BASH commands to compile and run the sample program.
• colnew_prb_output.txt, the output file.

List of Routines:

• COLNEW solves a multipoint boundary value problem using collocation.
• CONTRL is the driver for COLNEW.
• SKALE provides a scaling for the state variables.
• NEWMSH selects a mesh on which the solution is to be determined.
• CONSTS assigns values to various array constants.
• ERRCHK determines error estimates and tests error tolerances.
• LSYSLV controls the solution of linear systems.
• GDERIV constructs a row of the collocation matrix.
• VWBLOK constructs a group of NCOMP rows of the WI and VI matrices.
• GBLOCK constructs certain rows of the collocation matrix.
• APPSLN sets up a call to approximate the solution.
• APPROX evaluates the computes solution at a point.
• RKBAS evaluates a mesh-independent Runge-Kutta basis.
• VMONDE solves a Vandermonde linear system.
• HORDER determines the highest order derivatives of the current solution.
• DMZSOL computes DMZ in a blockwise manner.
• FCBLOK calls subroutines FACTRB and SHIFTB.
• FACTRB constructs a partial PLU factorization of a matrix.
• SHIFTB shifts rows in the current block.
• SBBLOK calls SUBFOR and SUBBAK so solve a block linear system.
• SUBFOR carries out the forward pass of substitution for the current block.
• SUBBAK carries out backsubstitution for the current block.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• DGEFA factors a double precision matrix by gaussian elimination.
• DGESL solves a linear system factored by DGEFA.
• DAXPY computes constant times a vector plus a vector.
• DDOT forms the dot product of two vectors.
• DSCAL scales a vector by a constant.
• IDAMAX finds the index of element having maximum absolute value.

You can go up one level to the FORTRAN77 source codes.