Runge's function is written as: fe) = '1+25x Generate four equidistantly spaced values (including the end points) of this function over the interval: (-0.75,0.75). Fit these data with a cubic spline with the not-a-knot end conditions. Show the resulting spline equations for each interval and determine the value of the function at x =0.5 using both Runge's function and the cubic spline equation. Compare the results by calculating the true percent relative error.

Runge's function is written as: fe) = '1+25x Generate four equidistantly spaced values (including the end points) of this function over the interval: (-0.75,0.75). Fit these data with a cubic spline with the not-a-knot end conditions. Show the resulting spline equations for each interval and determine the value of the function at x =0.5 using both Runge's function and the cubic spline equation. Compare the results by calculating the true percent relative error.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Runge's function is written as:
1+ 25x
Generate four equidistantly spaced values (including the end points) of this function over the
interval: [-0.75,0.75). Fit these data with a cubic spline with the not-a-knot end conditions.
Show the resulting spline equations for each interval and determine the value of the function at
x =0.5 using both Runge's function and the cubic spline equation. Compare the results by
calculating the true percent relative error.

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