Chapter 8

In the Moment of Heat

Folkmar Bornemann

Problem 8

8.1 A First Look · 8.2 Solving It Numerically · 8.3 Solving It Analytically · 8.4  Harder Problems

Solution is known to more than 10,002 digits.

Code

• FEMLAB
   
  • Table: 8.1 (2nd order elements), 8.1 (4th order elements)
  • Figure: 8.1
     
• Maple
   
  • Session: p. 177
     
• Mathematica (supporting code is included as initialization cells)
   
  • Sessions: p. 177, 179
  • Table: 8.3
  • The simple approximation of pp. 169/170
     
• MATLAB
   
  • Sessions: pp. 173, 174
  • Table: 8.2
  • Figures: 8.2 (left), 8.2 (right)
  • Commands: heat, richardson, theta
     
• MATLAB/INTLAB (download INTLAB)
   
  • Session: p. 179
  • Commands: IntervalNewton, theta, gradient of hull (install to a subdirectory @gradient in the working directory)

Historic Sources

•  Joseph Fourier: Théorie analytique de la chaleur, Didot, Paris 1822. §91 (misprinted as §84 in the 1st edition), §§171–177, §§179–180, §189, §§220–224, and §333.

This is a web page for the book:

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing. Society of Industrial and Applied Mathematics (SIAM), Philadelphia, 2004.

last modified: 06/09/04 21:08 +0200 (FB)