| The gradual abandonment of many types of well known experimental based physical models in favor of a more Universal Algebraic Theory: Part II - Specific examples Mike Mikalajunas1; 1CIME, iLe Perrot, Canada; PAPER: 339/Mathematics/Keynote (Oral) SCHEDULED: 12:45/Wed. 30 Nov. 2022/Arcadia 3 ABSTRACT: We will be presenting a very large amount of empirical results that were gathered from the numerical application of the unified theory of integration that was introduced in the first part of my entire presentation on a number of very specific mathematical models. This would include a general first order ODE followed by a second order PDE where a detailed empirical analysis of the data collected on each of these differential equations would lead to their complete integration in terms of generalized analytical solutions involving only the algebraic and elementary functions. We will also be presenting a series of Physical models which have been chosen very carefully just for demonstrating the applicability of our unified theory of integration into the Physical Sciences. These will include the equations for describing general linear elasticity and a very specific case of the Navier-Stokes equations corresponding to an incompressible fluid involving heat transfer and variable viscosity. For each of these physical models we will be developing a universal numerical process that would be based entirely on the general application of our specialized differential form representation of all mathematical equations for the exact integration of the corresponding set of PDEs in terms of only generalized exact analytical solutions that can satisfy a wide range of boundary conditions. |
