Predictor-Corrector Method for a First Order Equation

This program computes the solution Y(X) of the ordinary differential equation using the Adams Baskfort and Adams-Moulton methods:

dy(x)/dx = f(x,y)  for:  a < x< b  given the initial condition::
 

y (a) = ya
 

Program Notes
 

In order to use this program you will need to provide the following information:

 * Define the functionf( x,y ) using a Function FNF(x,y) = statement located at end of program.

 * Specify the input step size.

 * Define a tolerance for the local  error.

 * Specify the maximum number of correction cycles to be run.

Example

Solve the equation:

dy/dx = f(x,y) = x+y in the interval: (0,1)

for the initial condition, y(0) = 0

Downloads:

basic program - liberty basic - lbpcmfoe.bas

Test case:

PREDICTOR-CORRECTOR METH0D
FOR A FIRST ORDER EQUATION


ENTER INTERVAL OF INTEGRATION

A = 0
B = 1

INITIAL CONDITION

YA = 0

WANT STEPSIZE CONTROL (Y/N) ?N

INITIAL STEPSIZE

H = .25

TOLERANCE OF LOCAL ERROR X AS IN 1e-X = 7

MAXIMUM NUMBER OF

CORRECTION CYCLES ?3


SOLUTION
********


X = 0.25 Y =0.34016927e-1
X = 0.5  Y =0.14869947
X = 0.75 Y =0.36695803