So, Could It All Be True?

Abstract

The complexity of the proposed biomechanical model of the human stomach should not be underestimated. The governing system of nonlinear partial and ordinary differential equations has been solved numerically using ABS Technologies ^® platform. This employs hybrid finite difference and finite element methods of second order accuracy, with respect to spatial and time variables. Although the results reproduce qualitatively, and sometimes, quantitavely, in vivo and in vitro experiments, the fundamental question is whether or not these reflect the exact phenomena. This is essential in a modern day research environment with many simulation software supported by astounding graphical tools are available in the public domain. Given to a fervent investigator where little or no experience or understanding of how to apply them correctly, deceptive results can easily follow. This is common not only in a community of computational biologists, where opinions and decisions are dominated and dictated by biologists, but among engineers as well. Thus, a comparison of ten reputable analysis codes has shown an enormous discrepancy and variability of solutions to the very same mathematical problem. Possible explanations are: (i) “strong sensitivities of both a physical and computational nature”, and (ii) the “abuse”, driven by a desire to obtain a result at any cost, of the software pushed beyond the range of its validity (Cook et al. 2001).

How is error possible in mathematics?

Henry Poincare