微分方程 d 边界条件 v(0)有界,v(1)=0 构成本征值问题
Isoperimetric Problem (continued) Variational Formulism of Differential Equation (Approximation Method (Rayleigh-Ritz) Examples ©§ d dx x dy dx + λxy = 0 >.^ y(0)k., y(1) = 0 ¤ ¯K λi = µ 2 i , i = 1, 2, 3, · · · (µi´" l¼êJ0(x)1i":) ÐÒ´Lagrange¦f A ¼êyi(x) = CJ0 (µix)Ò´4¼ê ~þC±då^ Z 1 0 xy2dx = 1½Ñ C. S. Wu 1lù C©{ÐÚ
微分方程 d 边界条件 v(0)有界,v(1)=0 构成本征值问题 本征值λ i=1,2,3,… (是零阶贝塞耳函数J(x)的第i个正零点) 正好就是 Lagrange乘子 。相应本征函数v(x)=CJ0(1x)就是极值函数 常量C可以由约来条件/x
Isoperimetric Problem (continued) Variational Formulism of Differential Equation (Approximation Method (Rayleigh-Ritz) Examples ©§ d dx x dy dx + λxy = 0 >.^ y(0)k., y(1) = 0 ¤ ¯K λi = µ 2 i , i = 1, 2, 3, · · · (µi´" l¼êJ0(x)1i":) ÐÒ´Lagrange¦f A ¼êyi(x) = CJ0 (µix)Ò´4¼ê ~þC±då^ Z 1 0 xy2dx = 1½Ñ C. S. Wu 1lù C©{ÐÚ
微分方程 d 边界条件 v(0)有界,v(1)=0 构成本征值问题 本征值入;=12,1=1,2,3, (p是零阶贝塞耳函数J(x)的第i个正零点) 正好就是 Lagrange乘子 相应本征函数m(x)=CJ0(/x)就是极值函数 常量C可以由约束条件x2dx=1定出
Isoperimetric Problem (continued) Variational Formulism of Differential Equation (Approximation Method (Rayleigh-Ritz) Examples ©§ d dx x dy dx + λxy = 0 >.^ y(0)k., y(1) = 0 ¤ ¯K λi = µ 2 i , i = 1, 2, 3, · · · (µi´" l¼êJ0(x)1i":) ÐÒ´Lagrange¦f A ¼êyi(x) = CJ0 (µix)Ò´4¼ê ~þC±då^ Z 1 0 xy2dx = 1½Ñ C. S. Wu 1lù C©{ÐÚ
微分方程 d 边界条件 v(0)有界,v(1)=0 构成本征值问题 本征值入;=12,1=1,2,3, (p是零阶贝塞耳函数J(x)的第i个正零点) 正好就是 Lagrange乘子 相应本征函数v(x)=CJ(x)就是极值函数 。常量C可以由约束条件/xy2dx=1定出
Isoperimetric Problem (continued) Variational Formulism of Differential Equation (Approximation Method (Rayleigh-Ritz) Examples ©§ d dx x dy dx + λxy = 0 >.^ y(0)k., y(1) = 0 ¤ ¯K λi = µ 2 i , i = 1, 2, 3, · · · (µi´" l¼êJ0(x)1i":) ÐÒ´Lagrange¦f A ¼êyi(x) = CJ0 (µix)Ò´4¼ê ~þC±då^ Z 1 0 xy2dx = 1½Ñ C. S. Wu 1lù C©{ÐÚ
因为C2/x(x)dr=。i(山)=1
Isoperimetric Problem (continued) Variational Formulism of Differential Equation (Approximation Method (Rayleigh-Ritz) Examples Ï C 2 Z 1 0 xJ 2 0 (µix)dx = C 2 2 J 2 1 (µi) = 1 ¤± C = √ 2 J1(µi) ù§Ò¦Ñ 4¼ê yi(x) = √ 2 J1(µi) J0(µix) C. S. Wu 1lù C©{ÐÚ