DIFFER
Finite Difference Approximations to Derivatives

DIFFER is a FORTRAN77 library which determines the finite difference coefficients necessary in order to combine function values at known locations to compute an approximation of given accuracy to a derivative of a given order.

Licensing:

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

Languages:

DIFFER is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

DIVDIF, a FORTRAN77 library which uses divided differences to compute the polynomial interpolant to a given set of data.

Reference:

1. Ake Bjorck, Victor Pereyra,
   Solution of Vandermonde Systems of Equations,
   Mathematics of Computation,
   Volume 24, Number 112, October 1970, pages 893-903.

Source Code:

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

Examples and Tests:

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

List of Routines:

• DIFFER_BACKWARD computes backward difference coefficients.
• DIFFER_CENTRAL computes central difference coefficients.
• DIFFER_FORWARD computes forward difference coefficients.
• DIFFER_INVERSE returns the inverse of the DIFFER matrix.
• DIFFER_MATRIX computes the stencil matrix from the stencil vector.
• DIFFER_SOLVE solves for finite difference coefficients.
• DIFFER_STENCIL computes finite difference coefficients.
• INVERSE_ERROR determines the error in an inverse matrix.
• R8_FACTORIAL computes the factorial of N.
• R8MAT_FS factors and solves a system with one right hand side.
• R8MAT_MM multiplies two R8MAT's.
• R8MAT_MV multiplies a matrix times a vector.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• R8VEC2_PRINT prints an R8VEC2.
• R8VM_SL solves an R8VM linear system.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

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