e201401-901 · 2014. 12. 3. · =1/3+2/3*exp(-15*b4) ... 0 0.2 0.4 0.6 0.8 1 1.2 analytical...
TRANSCRIPT
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반응물(A)가 생성물(B)로 1차 가역 반응에 의하여 진행된다. ⇄ B정반응의 반응상수는 이며, 역반응의 반응상수는 이다. 위 반응에 대한 물질수지식을 세우면
− = − , − = −= 1, = 0, = 10, = 5라고 하면
− = 10 − 5 , − = 5 − 10참고로 해석해를 구하면 다음과 같다.= −m{1 − }= +m 1 − = −+
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= −m 1 − = 23 + 13= +m 1 − = 23 − 23
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− = 10 − 5 − = 5 − 10+ =
− = 10 − 5(1 − )− = 15 − 5
− = 5 − 10(1 − )− = 15 − 10
= − = −
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Alt+F11을 눌러 VBE를 실행한 뒤[삽입]-[모듈]을 클릭하여 새 모듈 생성
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funA = 5 – 15 * data2
funB = 10 – 15 * data4
data1 = , data2 = , data 3 = , data4 =
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Runge-Kutta4th order
= + 16 ( + 2 + 2 + )= ℎ ∙ ,= ℎ ∙ + , += ℎ ∙ + , += ℎ ∙ + ℎ, +
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=h*funA(B10,D10) 입력= ℎ ∙ ,= ℎ ∙ + , += ℎ ∙ + , += ℎ ∙ + ℎ, +
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= ℎ ∙ ,= ℎ ∙ + , += ℎ ∙ + , += ℎ ∙ + ℎ, +
=h*funA(B10+h/2,D10+E10/2) 입력
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= ℎ ∙ ,= ℎ ∙ + , += ℎ ∙ + , += ℎ ∙ + ℎ, +=h*funA(B10+h/2,D10+F10/2) 입력
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= ℎ ∙ ,= ℎ ∙ + , += ℎ ∙ + , += ℎ ∙ + ℎ, +=h*funA(B10+h,D10+G10) 입력
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= + 16 ( + 2 + 2 + )=D10+(E10+2*F10+2*G10+H10)/6 입력
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C19까지 자동 채우기
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D11셀에 ‘=C10’입력
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D20까지 자동 채우기
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E10:H10 영역 드래그
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E10:H19 영역을 자동 채우기로 셀을 채운다
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funB를 사용해 B의 값들도A와 같은 방식으로 셀의 값을 구한다
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해석해와 수치해 비교
= −m 1 − = 23 + 13= +m 1 − = 23 − 23
해석해 식
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=1/3+2/3*EXP(-15*B4) 입력
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C14까지 드래그하여 자동 채우기
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앞에서 구한 Runge-Kutta 값 가져오기
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D10:D20 영역을 드래그하여지정한 뒤 복사
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D4셀에서 오른쪽 마우스 클릭하여‘값 만 붙여넣기’ 선택
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오차율(%) = |수치해−해석해|해석해 100
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=ABS(D4-C4)/C4*100 입력
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E14까지 드래그하여 자동 채우기
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B의 오차도 A와 같은 방법으로 구한다(단, B의 첫 번째 오차는 분모가 0이므로 함수이용 ⅹ)
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Analytical solution of A Analytical solution of B
Numarical solution of A Numarical solution of B
해석해와 수치해 비교 그래프
해석해와 수치해 사이에 생기는 오차는h 값을 작게 하여 없앨 수 있다