restart:

# RUNGE-KUTTA (ORDER 4) ALGORITHM 5.2

# TO APPROXIMATE THE SOLUTION TO THE INITIAL VALUE PROBLEM:

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

# AT (N+1) EQUALLY SPACED NUMBERS 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 the Runge-Kutta Order Four 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(`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, `RUNGE-KUTTA FOURTH ORDER 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

# Use K1, K2, K3, K4 for K(1), K(2), K(3), K(4) resp.

K1 := H*F(T,W):

K2 := H*F(T+H/2.0, W+K1/2.0):

K3 := H*F(T+H/2.0, W+K2/2.0):

K4 := H*F(T+H,W+K3):

# Step 4

# Compute W(I)

W := W+(K1+2.0*(K2+K3)+K4)/6.0:

# Compute T(I)

T := A+I1*H:

# Step 5

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

od:

# Step 6

if OUP <> default then

fclose(OUP):

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

fi:

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IiIi

RUNGE-KUTTA FOURTH ORDER METHOD t w 0.000 0.5000000 0.200 0.8292933 0.400 1.2140762 0.600 1.6489220 0.800 2.1272027 1.000 2.6408227 1.200 3.1798942 1.400 3.7323401 1.600 4.2834095 1.800 4.8150857 2.000 5.3053630

JSFH