One of the oldest such attempts is due to John Stuart Mill (1996 [1843]), who presented a systematic account of causal inference that consisted of five different so-called "methods": the Method of Agreement, the Method of Difference, the Joint Method of Agreement and of Difference, the Method of Residues, and the Method Concomitant Variation.
Mill's method of difference captures an important kind of reasoning that is used frequently in biological experiments.
The method of difference potentials generalizes the method of Calderon's operators from PDEs to arbitrary difference equations and systems.
Next, we discretize the resulting boundary equation and solve it efficiently by the method of difference potentials (MDP).
We then employ the method of difference potentials to numerically solve the regularized problem with high-order accuracy over a domain with a curvilinear boundary.
While some of these "methods" pertain more to observation, the Method of Difference in particular is widely seen as encapsulating an important principle of scientific reasoning based on experiment.
Thus, Mill's method of difference asks us to look at two situations: one in which the phenomenon under investigation occurs, and one in which it does not occur.
In his method of difference, for example, one holds fixed every causal factor except one and checks to see whether the effect ceases to obtain when that one factor is removed.
This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP).
The quasi-static ABC for the magnetic field is obtained using the method of difference potentials, in the form of a discrete Calderon boundary equation with projection on the artificial boundary shaped as a parallelepiped.
For this purpose, the direct experimental method of difference dilatometry is applied in the present work in combination with differential scanning calorimetry (DSC) and scanning electron microscopy (SEM).
