sseuler:=proc(neqn,t0,u0,h,u,e) # # Procedure sseuler computes an ODE solution by the modified Euler # method for one step along the solution (by calls to derv to define # the ODE derivative vector). It also estimates the truncation error # of the solution, and applies this estimate as a correction to the # solution vector. # # Argument list # # neqn number of first order ODEs # # t0 initial value of independent variable # # u0 initial condition vector of length neqn # # h integration step # # u ODE solution vector of length neqn after # one modified Euler step # # e estimate of truncation error of the solu- # tion vector # # Type variables local ut0, ut, t, i: # # Declare arrays ut0:=array(1..neqn): ut:=array(1..neqn): # # Derivative vector at initial (base) point read "c:\\odelib\\maple\\ode1x1\\derv.txt": derv(neqn,t0,u0,ut0): # # First order (Euler) step for i from 1 to neqn do u[i]:=u0[i]+ut0[i]*h: end do: t:=t0+h: # # Derivative vector at advance point derv(neqn,t,u,ut): # # Truncation error estimate for i from 1 to neqn do e[i]:=(ut[i]-ut0[i])*h/2.0: end do: # # Second order (modified Euler) solution vector for i from 1 to neqn do u[i]:=u[i]+e[i]: end do: # # End of sseuler end: