예제: Stiffb 및 Stiffr를 위한 첨가된 야코비

함수 > 풀이 및 최적화 > 미분 방정식 풀이 > 예제: Stiffb 및 Stiffr를 위한 첨가된 야코비

Jacob 함수를 사용하여 상미분 방정식(ODE)에 대한 첨가된 야코비 행렬을 구한 다음 풀이 시스템 Stiffb 및 Stiffr의 입력 값으로 제공합니다.

1. 미지수가 네 개인 시스템을 정의합니다.

yi 변수는 x의 함수입니다.

2. 시스템의 상수를 정의합니다.

3. 초기치를 정의합니다.

4. 시스템의 우변에 해당하는 벡터 함수 D(x,y)를 정의합니다.

5. augment 함수를 사용하여 첨가된 야코비를 생성합니다.

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6. Stiffb 및 Stiffr 함수를 호출합니다.

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구한 행렬에는 점의 수와 미지수 네 개에 대한 해에 해당하는 5개 열이 들어 있습니다.

7. 구한 Stiffb 및 Stiffr 행렬에서 미지수 네 개에 대한 해를 추출합니다.

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8. 두 함수의 각 미지수에 대해 구한 해를 도표화하고 비교합니다.

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도표에서는 두 ODE 풀이 시스템이 동일한 해를 구했음을 보여줍니다.