From: cbmvax!uunet!ee.mu.OZ.AU!nsn
Message-Id: <9107010349.AA15942@munagin.ee.mu.OZ.AU>
To: lojban-list@snark.thyrsus.com
Cc: nsn@ee.mu.OZ.AU
Subject: Mex, 2nd installment
Organisation: Department of Electrical Engineering, University of Melbourne
Smiley-Convention: %^)
Date: Mon, 01 Jul 91 13:49:49 +1000
Status: RO


2nd Mex example: a differential equation thingy. From p. 81, Zill, I forget
the title.

p.81, Zill
di'e bipamoi lo'i papri be la zil.

Example
ni'o di'e mupli

Consider the problem
	y' = y - 1
	y(0) = 2.

.i ko pensi le nabmi po'u la'elu li sa'o 1boi .y'ybu du li - y'ybu 1
.ije li ma'o .y'ybu.boi 0 du li 2 li'u
{First argument of derivative: degree. 2nd: derivand. 3rd: variable of 
derivation. for example, dy/dx is sa'o 1boi y'ybu ge'a xy.}

Use Picard's method to find the approximations y\1, y\1, y\3, y\4.
.i ko pilno le tadji pe me'e la piKARD. lenu fakci le'i jbimi'u po'u
.y'ybuxipa ce'o .y'ybuxire ce'o .y'ybuxici ce'o .y'ybuxivo

Solution
ni'o di'e nabmi jalge
{a stuffed tanru, but ho hum}

By identifying x\0 = 0, y\0 (x) = 2,
.i fau ru'a lenu ge li xy.xi0 du li 0 ge li ma'o .y'ybu.xi0boi xy. du li 2

and f(t, y\[n-1] (t)) = y\[n-1] (t) - 1,
gi li ma'o fyboi tyboi ma'o .y'ybuxi vei ny.vu'u 1 ve'o ty du li - ma'o
.y'ybuxi vei ny.vu'u 1 ve'o tyboi 1 kei
{I probably stuffed up them subscripts bad, huh? Anyone know any better?}

equation (3) becomes
le cimoi be le'i mekso cu binxo me'o

y\n (x) = 2 + S [0 x] (y\[n-1] (t) - 1) dt, n in N
{S is integral sign, [0 x] are bounds of integration, N is set of natural
numbers}
ma'o du ma'o .y'ybu xinyboi xy + 2 ri'o - ma'o .y'ybuxi vei ny.vu'u 1 ve'o
tyboi 1boi ty ge'a 0bi'ixyboi va'o lenu li ny. cu cmima lo'i namcynaturale.
{First argument of integral: integrand, 2nd: variable of integration, 3rd:
integral bounds.}

Shit this is boring. Anyone got any comments on this text?