課程名稱︰ 中等數值方法
課程性質︰ 選修
課程教師︰ 李克強
開課學院： 工學院
開課系所︰ 化工系
考試日期（年月日）︰ 2015.06.22
考試時限（分鐘）： 120
試題 :
Intermediate Numerical Methods Final
1. Solve the following nonlinear ODE-BVP problem with shooting method. Write
down the corresponding canonical form for an ODE-IVP solver, together with
the auxiliary sensitivity equation. Write down the iteration scheme as
well.
2 2
y''+yy'+y = x , x∈[0,1]
B.C.'s: y(0)=0, y(1)+2y'(1)=3
2
2. Redo the previous problem with finite difference method accurate to O(h ),
but with the boundary conditions y(0)=0, y(1)=1. Write down the
corresponding difference equations for N=1, where N is the number of
interior points. In other words, h=0.5. Solve for y(0.5) by using
Newton-Raphson iteration scheme.