fd1d_heat_steady_test

fd1d_heat_steady_test, a C code which calls fd1d_heat_steady() to apply the finite difference method to estimate the solution of the steady state heat equation over a one dimensional region, which can be thought of as a thin metal rod.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Related Data and Programs:

fd1d_heat_steady, a C code which uses the finite difference method (FDM) to solve the steady (time independent) heat equation in 1D.

Source Code:

• fd1d_heat_steady_test.sh, runs all the tests.

• problem1.c, uses K(X) = 1, F(X) = 0, so the solution should be the straight line that connects the boundary values.
• problem1.sh, runs the test.
• problem1.txt, the output file.
• problem1_nodes.txt, the coordinates of the nodes.
• problem1_values.txt, the computed temperatures at the nodes.
• problem1.png, a PNG image of the solution.

• problem2.c, uses K(X) which is set to different constants over three subregions, and F(X) = 0.0, so the solution will be a piecewise linear function that connects the boundary values.
• problem2.sh, runs the test.
• problem2.txt, the output file.
• problem2_nodes.txt, the coordinates of the nodes.
• problem2_values.txt, the computed temperatures at the nodes.
• problem2.png, a PNG image of the solution.

• problem3.c, uses K(X) = 1, F(X) defines a heat source, so the solution can rise above the boundary values.
• problem3.sh, runs the test.
• problem3.txt, the output file.
• problem3_nodes.txt, the coordinates of the nodes.
• problem3_values.txt, the computed temperatures at the nodes.
• problem3.png, a PNG image of the solution.

• problem4.c, uses K(X) = 1, F(X) defines a heat source and a heat sink, so the solution can go above and below the boundary values.
• problem4.sh, runs the test.
• problem4.txt, the output file.
• problem4_nodes.txt, the coordinates of the nodes.
• problem4_values.txt, the computed temperatures at the nodes.
• problem4.png, a PNG image of the solution.