BVPSOL
Boundary Value Problem Solver

BVPSOL is 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, Lutz Weimann.

Licensing:

      Copyright     (c) Konrad-Zuse-Zentrum fuer
                        Informationstechnik Berlin (ZIB)
                        Takustrasse 7, D-14195 Berlin-Dahlem
                        phone : + 49/30/84185-0
                        fax   : + 49/30/84185-125
      

Languages:

BVPSOL is available in a FORTRAN77 version.

Related Data and Programs:

COLNEW, 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.

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:

Peter Deuflhard, Georg Bader, Lutz Weimann

Reference:

1. Josef Stoer, Roland Bulirsch,
   Introduction to Numerical Mathematics,
   Springer, 2002,
   ISBN: 038795452X,
   LC: QA297.S8213.

Source Code:

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

Examples and Tests:

• bvpsol_prb.f, a sample calling program.
• bvpsol_prb_data.txt, initialization data needed for the program.
• bvpsol_prb.sh, BASH commands to compile and run the sample program.
• bvpsol_prb_output.txt, the output file.
• bvpsol_prb_output_standard.txt, the output file as run on the original version of the code.

List of Routines:

• BVPSOL is a solver for highly nonlinear two point boundary value problems.
• BVPL carries out the local linear solver approach.
• BVPG carries out the global linear solver approach.
• BLFCNI computes the residual vector.
• BLSOLI seeks the least squares solution for the local approach.
• BGSOLI seeks the least squares solution for the global approach.
• BLPRCD prints the subcondition and sensitivity information.
• BLPRCV prints the relative accuracy information.
• BLSCLE scales the variables.
• BLLVLS evaluates level functions for the local approach.
• BGLVLS evaluates level functions for the global approach.
• BLRHS1 computes the condensed right hand side.
• BLRCRS carries out the recursive solution of a system of equations.
• BLPRJC projects the reduced component.
• BLDERA approximates boundary derivative matrices using differences.
• BLDERG estimates Wronskian matrices using differences.
• BLRK1G performs a rank-1 update of the Wronskian matrices.
• BLDFX1 - an explicit extrapolation integrator for nonstiff ODE's.
• BLDFSQ sets the stepsize sequence for DIFEX1.
• BLDFSC carries out scaling for DIFEX1.
• BLDFER evaluates the scaled root mean square error.
• BLDECC carries out a constrained least squares QR decomposition.
• BLSOLC performs a best constrained lienar least squares solution.
• MA28AD performs the LU factorization of A.
• MA28BD factorizes a matrix of known sparsity pattern.
• MA28CD solves a system factored by MA28AD or MA28BD.
• MA28DD sorts the user's matrix into the structure for the decomposed form.
• MA30AD solves a general sparse linear system.
• MA30BD LU factors the diagonal blocks of a matrix of known sparsity pattern.
• MA30CD solves A*x=b or A'x=b after factorization by MA30AD or MA30BD.
• MA30DD performs garbage collection.
• MC13D calls MC13E after dividing up the workspace.
• MC13E finds a symmetric permutation to block lower triangular form.
• MC20AD sorts the matrix into row order.
• MC20BD sorts the nonzeros of a sparse matrix by columns.
• MC21A calls MC21B after dividing up workspace.
• MC21B finds a row permutation to make the diagonal zero free.
• MC22AD reorders off-diagonal blocks according to the pivot.
• MC23AD performs block triangularization.
• MC24AD calculates the element growth estimate.
• MABLD1 contains block data.
• MABLD2 contains block data.
• MABLD3 contains block data.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• ZIBCONST sets machine constants.
• ZIBSEC returns the CPU time in seconds.

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