Dec 152017

A program plus examples of performing LIE ALGEBRA on differential equations. | |||
---|---|---|---|

File Name | File Size | Zip Size | Zip Type |

BLASIUS.DAT | 132 | 87 | deflated |

BLASIUS1.DAT | 192 | 150 | deflated |

BURGERS.DAT | 173 | 139 | deflated |

CANJUST.DAT | 622 | 278 | deflated |

EX258.DAT | 184 | 142 | deflated |

EXPU.DAT | 147 | 117 | deflated |

HEAT1.DAT | 373 | 228 | deflated |

HEATNL.DAT | 780 | 364 | deflated |

HODOGRAF.DAT | 283 | 222 | deflated |

IMPOSBLE.DAT | 386 | 220 | deflated |

KP.DAT | 224 | 179 | deflated |

LIE.DOC | 13132 | 5129 | deflated |

LIE.LIE | 54660 | 12042 | deflated |

MORELIE.DOC | 15596 | 5834 | deflated |

MULIE.EXE | 71646 | 48867 | deflated |

MZ.DAT | 477 | 226 | deflated |

NAVSTOKE.DAT | 630 | 280 | deflated |

README.1ST | 3132 | 1542 | deflated |

SCHWCHLD.DAT | 840 | 315 | deflated |

SPECIALC.DAT | 196 | 155 | deflated |

TRANSCEN.DAT | 198 | 135 | deflated |

WAVE2.DAT | 155 | 117 | deflated |

WAVE3.DAT | 198 | 153 | deflated |

# Download File LIE33.ZIP Here

## Contents of the README.1ST file

Program LIE for Lie analysis of differential equations on IBM type PCs

------------------------------------------------------------------------

by

A. K. Head

CSIRO Division of Materials Science and Technology

Melbourne Australia

Postal: Locked Bag 33, Clayton, Vic 3168, Australia

Phone: (03) 542 2861

Telex: AA 32945

Fax: (03) 544 1128

E-mail: [email protected]

Equipment

---------

Any IBM type PC with at least 256k of free memory.

Any version of DOS.

An attached printer is very useful.

Contents of disk

----------------

README.1ST This file.

MULIE.EXE The operating program.

LIE.DOC Read this for instructions.

MORELIE.DOC More information for those interested.

.DAT files Examples of differential equations you can run.

Read these to see how to write YOUR differential

equations and for the comments therein.

LIE.LIE Source code of LIE.

Update

------

Version 3.1

(1) LIE is wrtten in MUMATH, the symbolic mathematics language for

IBM type PCs. Previous versions have required you to have the MUMATH

system. By generous permission of Soft Warehouse Inc, authors and

owners of MUMATH, this is no longer necessary. A limited version of

MUMATH is combined with LIE to give MULIE.EXE which is a complete

stand-alone operating program. Portions of the software are

copyrighted by Soft Warehouse Inc, 3616 Harding Av., Suite 505,

Honolulu, Hawaii 96816 USA, and are used by permission on a gratis,

as-is basis with no liability or support.

(2) With the cumulative improvements to the heuristics of program

LIE, including a new Op that adds integrability conditions to the

defining equations, there is now little need for the user to intervene

( by low level MUMATH operations ) in the solution process. A lot of

the previous documentation was to aid in this intervention and this

has now been much reduced. The MUMATH manual is really what you would

need.

Version 3.2

A multinomial GCD package has been added. This aids in reducing the

size of expressions by detecting and dividing out inessential factors.

Larger problems can now be run without exhausting memory.

If your DE contains symbolic functions or constants then there may

be special values of these that lead to different Lie symmetries. This

may occur in two ways, that a factor which is divided out may be zero

in special cases, or, when splitting a "polynomial", that functions

taken as linearly independent may not be so in special cases.

Selective information on these possibilities can be shown by ( say )

SHOW#:LIST(A,B,K) where the list contains the names of functions and

constants of interest. ( This is turned off by SHOW#:FALSE, the

default value). See SPECIALC.DAT and the non-linear heat equation

HEATNL.DAT.

IMPORTANT: All derivatives of a symbolic function in the DE must

be written as explicit derivatives with respect to the argument of the

function else LIE will misfunction. See HEATNL.DAT.

Version 3.3

Extensions to factorization and to information shown by SHOW#.

------------------------------------------------------------------------

by

A. K. Head

CSIRO Division of Materials Science and Technology

Melbourne Australia

Postal: Locked Bag 33, Clayton, Vic 3168, Australia

Phone: (03) 542 2861

Telex: AA 32945

Fax: (03) 544 1128

E-mail: [email protected]

Equipment

---------

Any IBM type PC with at least 256k of free memory.

Any version of DOS.

An attached printer is very useful.

Contents of disk

----------------

README.1ST This file.

MULIE.EXE The operating program.

LIE.DOC Read this for instructions.

MORELIE.DOC More information for those interested.

.DAT files Examples of differential equations you can run.

Read these to see how to write YOUR differential

equations and for the comments therein.

LIE.LIE Source code of LIE.

Update

------

Version 3.1

(1) LIE is wrtten in MUMATH, the symbolic mathematics language for

IBM type PCs. Previous versions have required you to have the MUMATH

system. By generous permission of Soft Warehouse Inc, authors and

owners of MUMATH, this is no longer necessary. A limited version of

MUMATH is combined with LIE to give MULIE.EXE which is a complete

stand-alone operating program. Portions of the software are

copyrighted by Soft Warehouse Inc, 3616 Harding Av., Suite 505,

Honolulu, Hawaii 96816 USA, and are used by permission on a gratis,

as-is basis with no liability or support.

(2) With the cumulative improvements to the heuristics of program

LIE, including a new Op that adds integrability conditions to the

defining equations, there is now little need for the user to intervene

( by low level MUMATH operations ) in the solution process. A lot of

the previous documentation was to aid in this intervention and this

has now been much reduced. The MUMATH manual is really what you would

need.

Version 3.2

A multinomial GCD package has been added. This aids in reducing the

size of expressions by detecting and dividing out inessential factors.

Larger problems can now be run without exhausting memory.

If your DE contains symbolic functions or constants then there may

be special values of these that lead to different Lie symmetries. This

may occur in two ways, that a factor which is divided out may be zero

in special cases, or, when splitting a "polynomial", that functions

taken as linearly independent may not be so in special cases.

Selective information on these possibilities can be shown by ( say )

SHOW#:LIST(A,B,K) where the list contains the names of functions and

constants of interest. ( This is turned off by SHOW#:FALSE, the

default value). See SPECIALC.DAT and the non-linear heat equation

HEATNL.DAT.

IMPORTANT: All derivatives of a symbolic function in the DE must

be written as explicit derivatives with respect to the argument of the

function else LIE will misfunction. See HEATNL.DAT.

Version 3.3

Extensions to factorization and to information shown by SHOW#.

December 15, 2017
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