Initial value methods can also be used when it is important to determine the sensitivity of the solution to parameters. The sensitivity might be desired for studying the stability of the equations, especially when the solution bifurcates into more than one solution, or it might be required for parameter estimation. Knowing the sensitivity gives clues as to what experimental measurements are most important for verifying a mathematical model. As an example, suppose we want to know the sensitivity of the solution to problem b1 with respect to the Thiele modulus squared, f². Define the variables

and write the differential equation as

Next differentiate the equation with respect to f². Then add the following variables and equations.

These can be solved along with the original problem (on each iteration) or only after the proper s is found from the iterations. The result of this calculation is that we have c(x, f²) for some f², but we also know dc/df² at the same value of f². Then we can use

See also:

Description of Method

Multiple conditions

Turn the problem inside out

May work in only one direction