Math-RungeKutta

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RungeKutta.pm  view on Meta::CPAN

which all begin with the letters C<_rk_> so you should
avoid introducing variables beginning with these characters.

=head1 LUA

In the C<lua/> subdirectory of the install directory there is
I<RungeKutta.lua>, which is an exact translation of this Perl code into Lua.
The function names and arguments are unchanged.
Brief Synopsis:

 local RK = require 'RungeKutta'
 function dydt(t, y) -- the derivative function
   -- y is the table of the values, dydt the table of the derivatives
   local dydt = {}; ... ; return dydt
 end
 y = initial_y(); t=0; dt=0.4;  -- the initial conditions
 -- For automatic timestep adjustment ...
 while t < tfinal do
    t, dt, y = RK.rk4_auto(y, dydt, t, dt, 0.00001)
    display(t, y)
 end

lua/RungeKutta.lua  view on Meta::CPAN

--                        www.pjb.com.au                             --
--                                                                   --
--   This module is free software; you can redistribute it and/or    --
--          modify it under the same terms as Lua5 itself.           --
-- ----------------------------------------------------------------- --
local M = {} -- public interface
M.Version = '1.07'
M.VersionDate = '20aug2010'

-- Example usage:
-- local RK = require 'RungeKutta'
-- RK.rk4()

--------------------- infrastructure ----------------------
local function arr2txt(...) -- neat printing of arrays for debug use
	local txt = {}
	for e in ... do txt[#txt+1] = string.format('%g',e) end
	return table.concat(txt,' ') .. "\n"
end
local function warn(str)
	io.stderr:write(str,'\n')

lua/RungeKutta.lua  view on Meta::CPAN

--[[

=pod

=head1 NAME

RungeKutta.lua - Integrating Systems of Differential Equations

=head1 SYNOPSIS

 local RK = require 'RungeKutta'
 function dydt(t, y) -- the derivative function
   -- y is the table of the values, dydt the table of the derivatives
   -- the table can be an array (1...n), or a dictionary; whichever,
   -- the same indices must be used for the return table: dydt
   local dydt = {}; ... ; return dydt 
 end
 y = initial_y(); t=0; dt=0.4;  -- the initial conditions
 -- For automatic timestep adjustment ...
 while t < tfinal do
    t, dt, y = RK.rk4_auto(y, dydt, t, dt, 0.00001)

lua/test.lua  view on Meta::CPAN

--                                                                   --
--   This script is free software; you can redistribute it and/or    --
--          modify it under the same terms as Lua5 itself.           --
-- ----------------------------------------------------------------- --
local Version = '1.0  for Lua5'
local VersionDate  = '31jul2010';
local Synopsis = [[
program_name [options] [filenames]
]]

local RK = require 'RungeKutta'
--------------------------- infrastructure -----------------------
local eps = .000000001
function equal(x, y)  -- unused here
    if #x ~= #y then return false end
    local i; for i in pairs(x) do
        if math.abs(x[i]-y[i]) > eps then return false end
    end
    return true
end
-- use Test::Simple tests => 6;

lua/three-body.lua  view on Meta::CPAN

--                                                                   --
--   This script is free software; you can redistribute it and/or    --
--          modify it under the same terms as Lua5 itself.           --
-- ----------------------------------------------------------------- --
local Version = '1.0  for Lua5'
local VersionDate  = '1aug2010';
local Synopsis = [[
program_name [options] [filenames]
]]

local RK = require 'RungeKutta'

-- my ($maxcols, $maxrows);
-- eval 'require "Term/Size.pm"';
-- if ($@) {
--	$maxcols = `tput cols`;
--	if ($^O eq 'linux') { $maxrows = (`tput lines` + 0);
--	} else { $maxrows = (`tput rows` + 0);
--	}
-- } else {
--	($maxcols, $maxrows) = &Term::Size::chars(*STDERR);