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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Winter 2004 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Winter 2004 • Question 6

ODEs Consider the initial value problem of ODEs: \[ y'=f(x,y),\qquad y(a)=y_0. \tag {10} \] Describe the Trapezoidal Rule applied to this problem and analyze its local accuracy and its region of absolute stability.

Raw LaTeX

{ODEs}
Consider the initial value problem of ODEs:
\[
  y'=f(x,y),\qquad y(a)=y_0. \tag{10}
\]
Describe the Trapezoidal Rule applied to this problem and analyze its local accuracy
and its region of absolute stability.

Topic Tags

Absolute Stability and A-Stability Consistency, Stability, and Convergence Linear Programming and Optimization Quadrature Rules