Numerical Methods: Bisection, Newton-Raphson, Fixed-Point & Numerical Integration Accuracy

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Bracket Brannock Works' break-even volume, halve the interval 14 times, compare the actual error with the guaranteed bound and predict the number of steps in advance.
• Solve for the monthly rate of an equipment lease with Newton's method, using a central-difference slope, and watch it reach Excel's RATE in a handful of steps.
• Find a bond's yield to maturity with the secant method from two rough guesses, guard against division by zero and check the result against Excel's RATE.
• Resolve a revolver's interest circularity by iteration, then rewrite one break-even equation two ways and see one rearrangement converge and the other run off to the other root.
• Compare the four root-finders on one break-even equation: log₁₀ errors, iterations to tolerance and a chart that shows linear vs quadratic convergence at a glance.
• Build a project's NPV profile, run Newton's method on the NPV with its exact derivative and land on the same IRR that Excel's IRR function returns.
• Value a ramping, continuously discounted cash stream with the trapezoid rule for six step sizes, derive Simpson's rule with Richardson's trick and measure both methods' order of accuracy.
• Apply absolute, relative and residual stopping rules to the same iteration, see that they stop at different steps, and calculate the floor that floating point puts under any tolerance.