libdaestruct

Structural analysis of Differential Algebraic Equations (DAEs)

This library provides an implementation of Pryce' index reduction method[1]. In fact this method does not completely implement index reduction but yields the information about which equations and variables need to be differentiated up to which order to maintain an ODE.

Example

The following example demonstrates the usage of daestruct with the classic cartesian pendulum using the C-interface (for full code, see example/pendulum.c).

  const int dimension = 3;
  const int x = 0;
  const int y = 1;
  const int F = 2;

  struct daestruct_input* pendulum = daestruct_input_create(3);

  // x² + y² = 1
  daestruct_input_set(pendulum, x, 0, 0);
  daestruct_input_set(pendulum, y, 0, 0);

  // xF = der(der(x))
  daestruct_input_set(pendulum, x, 1, 2);
  daestruct_input_set(pendulum, F, 1, 0);

  // yF = der(der(y)) - g
  daestruct_input_set(pendulum, y, 2, 2);
  daestruct_input_set(pendulum, F, 2, 0);

  struct daestruct_result* result = daestruct_analyse(pendulum);

  const char* variables[] = {"x", "y", "F"};
  const char* equations[] = {"x² + y² = 1", "xF = der(der(x))", "yF = der(der(y)) - g" };

  for (int v = 0; v < dimension; v++)
    printf("'%s' needs to be differentiated %d times\n", variables[v], daestruct_result_variable_index(result, v));

  for (int eq = 0; eq < dimension; eq++)
    printf("'%s' needs to be differentiated %d times\n", equations[eq], daestruct_result_equation_index(result, eq));

  daestruct_input_delete(pendulum);
  daestruct_result_delete(result);

[1] Pryce, John D. "A simple structural analysis method for DAEs." BIT Numerical Mathematics 41.2 (2001): 364-394. http://link.springer.com/article/10.1023/A:1021998624799