Linear Recursion Method

In Vol. 2 (Thomas, 2017) we outlined a strategy for computing results for decision process theory models. This is expanded on in the Stationary Ownership Model. The starting point is the idea that meaningful results from the theory on decisions can be obtained by considering steady state phenomena, like the idea of studying AC circuits in electrical engineering. The resultant equations are non-linear elliptic partial differential equations. The problem is that such equations currently don’t admit a simple numerical solution strategy.

We would like an approach that is general assuming only that the behaviors are stationary. To that end we attack in some detail the needed numerical approach needed to carry out that program. In this white paper we explore several relevant aspects:

  • The need to solve the non-linear elliptic equations more effectively than what can be done by the method of lines. The issues are illustrated with a Wolfram Mathematica CDF notebook. We suggest using the linear recursion method.
  • As part of the approach using the method of lines, we need to have an effective way to deal with covariant gauge conditions, illustrated with a Wolfram CDF notebook.
  • To apply the linear recursion method to decision process theory, we need to have a linearized form. We first show what the form is in the general theory.
  • We then show the form specialized to decision process theory.

This white paper is a work in progress, leaving many open issues that need to be explored further.

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