http://w.atwiki.jp/yamaoka/ CIP法 ja 2020-05-29T19:11:38+09:00 1590747098 https://w.atwiki.jp/yamaoka/pages/14.html **メニュー #recent(10) 2020-05-29T19:11:38+09:00 1590747098 https://w.atwiki.jp/yamaoka/pages/13.html *CIP法 $$F(x)=a(x-x_i)^3+b(x-x_i)^2+c(x-x_i)+d$$ $$\displaystyle a=-2\frac{f^n_i-f^n_{i-1}}{\Delta x^3}+\frac{g^n_i+g^n_{i-1}}{\Delta x^2}$$ $$\displaystyle b=-3\frac{f^n_i-f^n_{i-1}}{\Delta x^2}+\frac{2g^n_i+g^n_{i-1}}{\Delta x}$$ $$c =g^n_i$$ $$d=f^n_i$$ *2次元CIP法 $$F(x,y)=C_{3,0}(x-x_i)^3+C_{2,1}(x-x_i)^2(y-y_j)+C_{2,0}(x-x_i)^2\\$$ $$+C_{1,2}(x-x_i)(y-y_j)^2+C_{1,1}(x-x_i)(y-y_j)+C_{1,0}(x-x_i)\\$$ $$+C_{0,3}(y-y_j)^3+C_{0,2}(y-y_j)^2+C_{0,1}(y-y_j)+C_{0,0}$$ $$C_{0,0}=f_{i,j}$$ $$C_{1,0}=g_{i,j}$$ $$C_{0,1}=h_{i,j}$$ $$C_{3,0}=-2\frac{f_{i,j}-f_{i-1,j}}{\Delta x^3}+\frac{g_{i,j}+g_{i-1,j}}{\Delta x^2}$$ $$C_{2,0}=-3\frac{f_{i,j}-f_{i-1,j}}{\Delta x^2}+\frac{2g_{i,j}+g_{i-1,j}}{\Delta x}$$ $$C_{0,3}=-2\frac{f_{i,j}-f_{i,j-1}}{\Delta y^3}+\frac{h_{i,j}+h_{i,j-1}}{\Delta y^2}$$ $$C_{0,2}=-3\frac{f_{i,j}-f_{i,j-1}}{\Delta y^2}+\frac{2h_{i,j}+h_{i,j-1}}{\Delta y}$$ $$C_{2,1}=-\frac{f_{i,j}-f_{i-1,j}-f_{i,j-1}-f_{i-1,j-1}}{\Delta x^2\Delta y}+\frac{g_{i,j}+g_{i,j-1} 2015-08-01T08:37:52+09:00 1438385872 https://w.atwiki.jp/yamaoka/pages/1.html *CIP法 $$F(x)=a(x-x_i)^3+b(x-x_i)^2+c(x-x_i)+d$$ $$\displaystyle a=-2\frac{f^n_i-f^n_{i-1}}{\Delta x^3}+\frac{g^n_i+g^n_{i-1}}{\Delta x^2}$$ $$\displaystyle b=-3\frac{f^n_i-f^n_{i-1}}{\Delta x^2}+\frac{2g^n_i+g^n_{i-1}}{\Delta x}$$ $$c =g^n_i$$ $$d=f^n_i$$ *2次元CIP法 $$F(x,y)=C_{3,0}(x-x_i)^3+C_{2,1}(x-x_i)^2(y-y_j)+C_{2,0}(x-x_i)^2\\$$ $$+C_{1,2}(x-x_i)(y-y_j)^2+C_{1,1}(x-x_i)(y-y_j)+C_{1,0}(x-x_i)\\$$ $$+C_{0,3}(y-y_j)^3+C_{0,2}(y-y_j)^2+C_{0,1}(y-y_j)+C_{0,0}$$ $$C_{0,0}=f_{i,j}$$ $$C_{1,0}=g_{i,j}$$ $$C_{0,1}=h_{i,j}$$ $$C_{3,0}=-2\frac{f_{i,j}-f_{i-1,j}}{\Delta x^3}+\frac{g_{i,j}+g_{i-1,j}}{\Delta x^2}$$ $$C_{2,0}=-3\frac{f_{i,j}-f_{i-1,j}}{\Delta x^2}+\frac{2g_{i,j}+g_{i-1,j}}{\Delta x}$$ $$C_{0,3}=-2\frac{f_{i,j}-f_{i,j-1}}{\Delta y^3}+\frac{h_{i,j}+h_{i,j-1}}{\Delta y^2}$$ $$C_{0,2}=-3\frac{f_{i,j}-f_{i,j-1}}{\Delta y^2}+\frac{2h_{i,j}+h_{i,j-1}}{\Delta y}$$ $$C_{2,1}=-\frac{f_{i,j}-f_{i-1,j}-f_{i,j-1}-f_{i-1,j-1}}{\Delta x^2\Delta y}+\frac{g_{i,j}+g_{i,j-1} 2018-02-12T13:50:00+09:00 1518411000