restart:

# EULER'S ALGORITHM 5.1

# TO APPROXIMATE THE SOLUTION OF THE INITIAL VALUE PROBLEM:

# Y' = F(T,Y), A<=T<=B, Y(A) = ALPHA,

# AT N+1 EQUALLY SPACED POINTS IN THE INTERVAL [A,B].

# INPUT: ENDPOINTS A,B: INITIAL CONDITION ALPHA: INTEGER N.

# OUTPUT: APPROXIMATION W TO Y AT THE (N+1) VALUES OF T.

print(`This is Euler's Method.`):

print(`Input the function f(t,y) in terms of t and y`):

print(`For example: y-t^2+1`):

F := scanf(`%a`)[1]:print(`your function f(t,y) = `):print(F):

F := unapply(F,t,y):

OK := FALSE:

while OK = FALSE do

print(`Input left and right endpoints separated by blank`):

A := scanf(`%f`)[1]:print(`a = `):print(A):

B := scanf(`%f`)[1]:print(`b = `):print(B):

if A >= B then

print(`Left endpoint must be less than right endpoint`):

else

OK := TRUE:

fi:

od:

print(`Input the initial condition`):

ALPHA := scanf(`%f`)[1]:print(`y(a) = `):print(ALPHA):

OK := FALSE:

while OK = FALSE do

print(`Input a positive integer for the number of subintervals`):

N := scanf(`%d`)[1]:print(`N = `):print(N);

if N <= 0 then

print(`Number must be a positive integer`):

else

OK := TRUE:

fi:

od:

if OK = TRUE then

print(`Choice of output method:`):

print(`1. Output to screen`):

print(`2. Output to text file`):

print(`Please enter 1 or 2`):

FLAG := scanf(`%d`)[1]:print(`Your choice is `):print(FLAG):

if FLAG = 2 then

print(`Input the file name in the form - drive:\134\134name.ext`):

print(`For example A:\134\134OUTPUT.DTA`):

NAME := scanf(`%s`)[1]:print(`File name is `):print(NAME):

OUP := fopen(NAME,WRITE,TEXT):

else

OUP := default:

fi:

fprintf(OUP, `EULERS METHOD\134n\134n`):

fprintf(OUP, ` t w\134n\134n`):

# Step 1

H := (B-A)/N:

T := A:

W := ALPHA:

fprintf(OUP, `%5.3f %11.7f\134n`, T, W):

# Step 2

for I1 from 1 to N do

# Step 3

# Compute W(I)

W := W+H*F(T, W):

# Compute T(I)

T := A+I1*H:

# Step 4

fprintf(OUP, `%5.3f %11.7f\134n`, T, W):

od:

# Step 5

if OUP <> default then

fclose(OUP):

print(`Output file`,NAME,` created successfully`):

fi:

SThUaGlzfmlzfkV1bGVyJ3N+TWV0aG9kLkc2Ig==

SU5JbnB1dH50aGV+ZnVuY3Rpb25+Zih0LHkpfmlufnRlcm1zfm9mfnR+YW5kfnlHNiI=

STVGb3J+ZXhhbXBsZTp+eS10XjIrMUc2Ig==

STh5b3VyfmZ1bmN0aW9ufmYodCx5KX49fkc2Ig==

LChJInlHNiIiIiIqJEkidEdGJCIiIyEiIkYlRiU=

SVJJbnB1dH5sZWZ0fmFuZH5yaWdodH5lbmRwb2ludHN+c2VwYXJhdGVkfmJ5fmJsYW5rRzYi

SSVhfj1+RzYi

JCIiIUYj

SSVifj1+RzYi

JCIiIyIiIQ==

STxJbnB1dH50aGV+aW5pdGlhbH5jb25kaXRpb25HNiI=

SSh5KGEpfj1+RzYi

JCIiJiEiIg==

SVhJbnB1dH5hfnBvc2l0aXZlfmludGVnZXJ+Zm9yfnRoZX5udW1iZXJ+b2Z+c3ViaW50ZXJ2YWxzRzYi

SSVOfj1+RzYi

IiM1

STlDaG9pY2V+b2Z+b3V0cHV0fm1ldGhvZDpHNiI=

STQxLn5PdXRwdXR+dG9+c2NyZWVuRzYi

STcyLn5PdXRwdXR+dG9+dGV4dH5maWxlRzYi

STRQbGVhc2V+ZW50ZXJ+MX5vcn4yRzYi

STBZb3VyfmNob2ljZX5pc35HNiI=

IiIi

EULERS METHOD t w 0.000 0.5000000 0.200 0.8000000 0.400 1.1520000 0.600 1.5504000 0.800 1.9884800 1.000 2.4581760 1.200 2.9498112 1.400 3.4517734 1.600 3.9501281 1.800 4.4281538 2.000 4.8657845

JSFH