A Scheme That Works

This instability can be eliminated by calculating the slope of the straight-line approximation not at x, where the value of y is already known, but at the future time x + delx. Therefore, instead of 

OPEN RESULTS.PRN FOR OUTPUT AS 1 results to a file for plotting PRINT YEARS, PC02  

PRINT x, y PRINT 1, x, y FOR nx = 1 TO nstep GOSUB EQUATIONS GOSUB STEPPER G0SU8 PRINTER NEXT nx CLOSE 1 END 

PRINTER Subroutine writes a file for subsequent plotting 

Program DGC02 implements this solution, which is called the reverse Euler method. The only change in the code is in the expression foryp in the subroutine EQUATIONS. 

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