Runge-Kutta Method for A First Order Equation

This program will compute the solution of the Cauchy problem for the first order differential equation using a 4th order Runge-Kutta method:

dy/dx=f(Y(x),x) ,  X >A

Y (A) = Ya
 

Program Notes

To run this program, you must define the function f(Y,X) in the function statement.
 

Example:

Compute the solution to the Cauchy problem:

dy/dx = x + y ,  x > 0

Y(0) = 0

Downloads:

basic program (liberty basic) lbrkmse.bas

Test Case:

Notice that the problem will not converge without the use of step size control:

RUNGE-KUTTA METH0D FOR A
SYSTEM OF EQUATIONS

ENTER LIMITS OF INTEGRATION
A = 0
B = 1
YA = 0
INITIAL STEPSIZE
H = .5
LOCAL ERROR TOLERANCE X AS IN 1E-X
X = 7
STEPSIZE CONTROL (Y/N) ?Y

SOLUTION
********
X = 0  Y = 0
X = 0.0625   Y = 0.19944589e-2
X = 0.125  Y = 0.8148453e-2
X = 0.1875   Y = 0.18730249e-1
X = 0.25   Y = 0.34025417e-1
X = 0.3125   Y = 0.54337941e-1
X = 0.375  Y = 0.79991415e-1
X = 0.4375   Y = 0.1113303
X = 0.5  Y = 0.14872127
X = 0.5625   Y = 0.19255466
X = 0.625  Y = 0.24324596
X = 0.6875   Y = 0.30123747
X = 0.75   Y = 0.36700002
X = 0.8125   Y = 0.44103479
X = 0.875  Y = 0.52387529
X = 0.9375   Y = 0.61608946
X = 1  Y = 0.71828183
END OF EXECUTION