
mlde(1)                      Khoros                       mlde(1)

PROGRAM
     mlde - solves a system of linear ODE's

SYNTAX
     mlde

     -i1            coefficient matrix

     -i2            constant driving term vector

     -i3            initial value vector

     -o             numerical solution file

     [-t0]          initial time

     [-tf]          final time

     [-h]           time step

     [-V]           Gives the version for mlde

     [-U]           Gives the usage for mlde

     [-P]           Prompts for command line options

     [-A [file1]]   Creates the answer file called mlde.ans or
                    file1

     [-a [file1]]   Uses mlde.ans or file1 as the answer file

DESCRIPTION
     solves a system of constant coefficient linear ordinay dif-
     ferential equations with constant driving functions.  As
     input, it takes a matrix that represents the constant coef-
     ficients, a vector that contains the constant driving func-
     tions and a vector that contains the initial conditions.
     With these inputs, the system is defined by the equation:

             x' = Ax + b

     where x',x, and b are n-vectors and A is an n x m matrix
     such that m is less than or equal to n.

     If the constant driving function vector (b) or the initial
     condition vector is not specified, then they will be set to
     zero.  The coefficient matrix is a required argument.

     mlde will output data in one of two formats.  The default
     format is an ASCII readable, columnar data file formatted
     such that the first column is the time data and subsequent
     columns correspond to x1, x2, ... as given in the x vector
     described above.  The second format that can be output is
     the VIFF image format that is used by most Khoros applica-
     tions.  The option is allowed to facilitate plotting with
     Xprism2.  The data will be formatted in the VIFF file such
     that band #0 contains a vector of data for x1, band #1 con-
     tains a vector of data for x2, and so forth.  At this time,
     the time data is not stored in the VIFF structure.

     mlde solves the system of linear ordinary differential equa-
     tions by using the Classic 4th order Runge-Kutta method.
     This method uses the equations

             k1 = h*f'(xn,yn)
             k2 = h*f'(xn + h/2, yn + k1/2)
             k3 = h*f'(xn + h/2, yn + k2/2)
             k4 = h*f'(xn + h, yn + k3)

             y(n+1) = yn + k1/6 + k2/3 + k3/3 + k4/6

     where yn = y(n) and xn = x(n), to progress from xn to xn+h.

REQUIRED ARGUMENTS
     -i1    type: infile
            desc: coefficient matrix

     -i2    type: infile
            desc: constant driving term vector

     -i3    type: infile
            desc: initial value vector

     -o     type: outfile
            desc: numerical solution file

OPTIONAL ARGUMENTS
     -t0    type: float
            desc: initial time
            default: 0
            bounds: no range checking

     -tf    type: float
            desc: final time
            default: 1
            bounds: no range checking

     -h     type: float
            desc: time step
            default: 0.1
            bounds: no range checking

EXAMPLES
SEE ALSO
     intro(1), verror(3), vgparms(3), vutils(3), lmlde(3)

RESTRICTIONS
COPYRIGHT
     Copyright 1992, University of New Mexico.  All rights
     reserved.

Khoros                    Release: 1.0                          1

