Computational Physics with Hybrid Symbolic-Numeric Methodology for Multidisciplinary Applications

We used computer aided symbolic computation in our previous papers[1,2] to explore solutions of partial differential equations in a way that involves a synergistic application of symbolic and numeric methodologies. Here we review the results thus far and present a few examples of this emerging methodology. This continued development is presented with the hope of inspiring new thought in utilizing hybrid symbolic and numeric manipulation for solving the equations of mathematical physics from a fundamental perspective. We see an opportunity to revisit the very foundations of scientific computing armed with new symbolic and numeric computational tools that complement the numerical power of modern machines.