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 differential equations with constant driving functions. As input, it takes a matrix that represents the constant coefficients, a vector that contains the constant driving functions 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 applications. 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 contains 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 equations 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.