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Efficient Root Finding Techniques for Computational Engineering Analysis

Learn how to utilize iterative solutions and graph-based root finding methods for accurate results in engineering computations. Discover the steps for using a graph, bisection routine, and goal seek function to efficiently locate roots within specified tolerances.

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Efficient Root Finding Techniques for Computational Engineering Analysis

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  1. ME 142Engineering Computation I Root Finding & Iterative Solutions

  2. Using a Graph to Find Roots • Approximate process • May be used as a starting process to an iterative method • May want to refine axis max/min values to focus on plot on area of interest

  3. Using a Graph to Find Roots

  4. Bisection Routine • Begin with initial guess: xlow, xhi • Calculate corresponding f(x): f(xlow), f(xhi) • f(xlow)*f(xhi)<0, to ensure root lies within interval • Estimate Root and calculate corresponding f(xroot) • Determine subinterval of root • If f(xlow)*f(xroot)<0, set xhi=xroot • If f(xlow)*f(xroot)>0, set xlow=xroot • Repeat Steps 3-4 until desired tolerance is reached

  5. Bisection Routine Determine subinterval of root If f(xlow)*f(xroot)<0, set xhi=xroot If f(xlow)*f(xroot)>0, set xlow=xroot

  6. Goal Seek Function • Begin with initial guess • “x” value • Define function, f(x), related to initial guess • Use Goal Seek function to find root

  7. Goal Seek Function

  8. Goal Seek Function • Accuracy of Goal Seek function can be controlled in Excel Options • You may need to set the following: • Maximum Iterations • Maximum Change

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