NUMERICAL ANALYSIS 10TH EDITION BY
BURDEN FINAL PAPER 2026 SOLVED
QUESTIONS WITH FULL SOLUTION ALREADY
PASSED
◉ List three characteristics that you would use to decide on the best
numerical method for a given problem (3 points)..
Answer: Solution a) Number of initial guess or starting point
b) Rate of convergence
c) Stability: will it always converge
d) Accuracy and precision
◉ Write an equation to express total error of a numerical solution if
there is no analytical solution to the problem (2 points)..
Answer: Solution: If not analytical solution and hence no true value,
define approximate error (Ea)based on iterative process of solution:
Ea = Current Approximation - Previous Approximation Approximate
percent relative error:
Ea=(current approx-previous approx)/current approx
◉ Why does each numerical derivative method result in reduction of
total error between the estimate and true value as the step size is
, reduced, however the total error increases when the step size
becomes too small (2 points)?.
Answer: Total error is sum of truncation error and round off error.
Usually round-off errors do not predominate so as the step size is
reduced total error decrease due to reduction in truncation error
Truncation error decreases while round-off error increases with
smaller step size resulting in
higher total error for too small step sizes.
◉ List three ways that error associated with Taylor series estimation
of a function can be minimized.
Answer: Solution: a) Reducing the step size b) Increasing the order
of Taylor series (add more terms) . c) Make the equation more linear.
◉ What are the principal two advantages of Newton-Raphson
method compared to Secant method (4 points)?.
Answer: Newton-Raphson method requires only one initial guess
while the secant method requires 2 initial guesses. b) It converges
faster as compared to secant method. c) Is more accurate as
compared to secant method.
◉ Given the following equation: f(x)=5e^x+(2/x)(e^x-1)
Determine if numerical method or analytical method should be used
to solve this problem. Explain your answer. If numerical method
BURDEN FINAL PAPER 2026 SOLVED
QUESTIONS WITH FULL SOLUTION ALREADY
PASSED
◉ List three characteristics that you would use to decide on the best
numerical method for a given problem (3 points)..
Answer: Solution a) Number of initial guess or starting point
b) Rate of convergence
c) Stability: will it always converge
d) Accuracy and precision
◉ Write an equation to express total error of a numerical solution if
there is no analytical solution to the problem (2 points)..
Answer: Solution: If not analytical solution and hence no true value,
define approximate error (Ea)based on iterative process of solution:
Ea = Current Approximation - Previous Approximation Approximate
percent relative error:
Ea=(current approx-previous approx)/current approx
◉ Why does each numerical derivative method result in reduction of
total error between the estimate and true value as the step size is
, reduced, however the total error increases when the step size
becomes too small (2 points)?.
Answer: Total error is sum of truncation error and round off error.
Usually round-off errors do not predominate so as the step size is
reduced total error decrease due to reduction in truncation error
Truncation error decreases while round-off error increases with
smaller step size resulting in
higher total error for too small step sizes.
◉ List three ways that error associated with Taylor series estimation
of a function can be minimized.
Answer: Solution: a) Reducing the step size b) Increasing the order
of Taylor series (add more terms) . c) Make the equation more linear.
◉ What are the principal two advantages of Newton-Raphson
method compared to Secant method (4 points)?.
Answer: Newton-Raphson method requires only one initial guess
while the secant method requires 2 initial guesses. b) It converges
faster as compared to secant method. c) Is more accurate as
compared to secant method.
◉ Given the following equation: f(x)=5e^x+(2/x)(e^x-1)
Determine if numerical method or analytical method should be used
to solve this problem. Explain your answer. If numerical method
