上海交通大学：《复杂系统动力学计算机辅助分析》课程教学资源_Chapter 7_chap7-Numerical Methods in Dynamics

〉 t=t+△t v(t)=s(t),(t)=r(t) Step 3: Solve W=f() i= of(v)y for u(t),(t) 8v Return to step 2 for next time step to=t v(to)=v(t),i(to)=i(t)

Solve for u(t),u(t) u  f (v) v v f v u     ( ) Step 3: Return to step 2 for next time step t  t 0 t  t  t v(t)  s(t), v(t)  r(t) 0 ( ) ( ), ( ) ( ) 0 0 v t  v t v t  v t

2.Direct Integration Step 1: Fort=0v(0),(0) are given Solve (u(0),v(0))=0 D(0)i(0)=V(0)-Φ(0)y(0) u(0),(0) Step 2: Calculate M,Q,:Y Solve equations gg >i=f(g,9,t)元

Solve equations                     T A M q Q q q  0 q f(q,q,t) t0  0 v(0), v(0) (u(0),v(0))  0 (0)u(0) V(0) (0)v(0) u  v  u(0), u(0) , , , Μ Q q A 