Question

1. According to the Existence and Uniqueness theorem, the differential equation
   

   (t−5)y′+ysin(t)=5t

   
   necessarily has a unique solution on the interval 0<t≤5.
   

   TRUE

   FALSE

2. A numerical method is said to converge if its approximate solution values for a differential equation y′=f(t,y),
   

   y1,y2,...,yn,

   
   approach the true solution values
   

   ϕ(t1),ϕ(t2),...,ϕ(tn),

   
   as the stepsize h→∞.
   

   TRUE

   FALSE

3. If a numerical method has a global truncation error that is proportional to the nth power of the stepsize, then it is called an nth order method.
   

   TRUE

   FALSE

4. The fourth-order four stage Runge-Kutta method uses five approximations of the slope of the function along each numerical interval [tn,tn+1] and has a global truncation error proportional to fourth power of the timepoints, tn^4.
   

   TRUE

   FALSE

Answer 1

D false Truue mue