Plasma Application Modeling, POSTECH

# Plasma Application Modeling, POSTECH

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## Plasma Application Modeling, POSTECH

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1. Plasma Application Modeling, POSTECH ODE by using Modified Euler Method 2005. 9. 27. G.J. Kim

2. Plasma Application Modeling, POSTECH Problem 8 Solve the following ODE by using second-order modified Euler method without iteration through the shooting method

3. Plasma Application Modeling, POSTECH Exact Solution Exact Solution

4. Plasma Application Modeling, POSTECH Code subroutine ode(y0,z0,yl,x,y,z) real y0,z0 real x(100),y(100),z(100) real dx integer N common /a/ N,dx y(1) = y0 z(1) = z0 do 400 i = 2,N z(i) = z(i-1)+dx*dz(x(i-1),y(i-1),z(i-1)) y(i) = y(i-1)+dx*dy(x(i-1),y(i-1),z(i-1)) z(i) = z(i-1)+0.5*dx* ( dz(x(i),y(i),z(i)) + dz(x(i-1),y(i-1),z(i-1)) ) y(i) = y(i-1)+0.5*dx* ( dy(x(i),y(i),z(i)) + dy(x(i-1),y(i-1),z(i-1)) ) 400 continue yl = y(N) end subroutine shoot(Y0,YL,x,y,z) real Y0,YL real yll,b,slope,o1,o2,t1,t2 real error b = 0 yll = YL + 100 t1 = 0.0 t2 = 1.0; call ode(Y0,t1,o1,x,y,z) call ode(Y0,t2,o2,x,y,z) slope = (o1 - o2)/(t1 - t2) do 300 i = 1,100 b = b + (YL-yll)/slope; print *,'b = ',b call ode(Y0,b,yll,x,y,z) error = abs(YL-yll) print *,'error = ',error,i if(error .LT. 0.001) go to 301 300 continue 301 end

5. Plasma Application Modeling, POSTECH Euler Method solution error

6. Plasma Application Modeling, POSTECH Modified Euler Method (no iteration) solution error

7. Plasma Application Modeling, POSTECH Compare h=0.125 h=0.25 h=0.0625 h=0.03125