전자 전기 공학과 최선미 Example 9.2 a) Solve using the forward Euler method using h=0.01 for o this part by hand calculation. b ) Repeat the same for h=0,01,0,001,0,0001 on a computer for Evaluate errors of the three calculations by comparison to the analytical solution given by The Exact Solution is

REAL T,Y,H,EXACT,Error PARAMETER(U=20) PRINT *,'ODE BY Forword EULER METHOD' DATA T,Y,H /0.0,5.0,0.01/ PRINT *,' T Y EXAXCT ERROR' 1 FORMAT(F10.5,F10.5,F10.5,F10.5) OPEN(U,FILE='ANSWER1.TXT') WRITE(U,*)'ODE BY Forword EULER METHOD' WRITE(U,*)' T Y EXACT ERROR' WRITE(U,*)' ' DO 10 N=1,9 Y=Y+H*(7*EXP(-0.5*T)-20*Y) T=T+H EXACT=5*EXP(-20*T)+7/19.5*(EXP(-0.5*T)-EXP(-20*T)) Error=Y-EXACT PRINT 1,T,Y,EXACT,Error WRITE(U,1)T, Y,EXACT,Error 10 CONTINUE STOP END

ODE BY Forword EULER METHOD T Y EXACT ERROR ODE BY Forword EULER METHOD T Y EXACT ERROR ODE BY Forword EULER METHOD T Y EXACT ERROR Forward Euler dt=0.01) Forward Euler dt=0.0001)Forward Euler dt=0.001)

By using Fortran

ErrorAll Figure By using Fortran

By explicit Euler dt=0.0001) By explicit Euler dt=0.0005) By using Mathematica Forward Euler dt=0.01)Forward Euler dt=0.001) Forward Euler dt=0.0001)

ErrorAll Figure By using Mathematica