A. T. Ringler

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We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence operator. As a practical application, we show how the operators can be used to symbolically compute local conservation laws(More)
Algorithms for the symbolic computation of conserved densities, fluxes, generalized symmetries, and recursion operators for systems of nonlin-ear differential-difference equations are presented. In the algorithms we use discrete versions of the Fréchet and variational derivatives, as well as discrete Euler and homotopy operators. The algorithms are(More)
The end goal of any solid Earth study is to better constrain physical parameters of the Earth (e.g. viscosity, temperature, and mineral composition). As we are unable to directly measure many of these quantities, past a few kilometers in depth, we must content ourselves with indirect estimates by way of experiment and theory. Just as geochemists do this by(More)
After learning the appropriate mathematical methods and working out examples by hand, our team planned to write software that would implement the Homotopy Operator for polynomial and transcendental equations on the jet space. This code will be integrated into existing Mathematica code, and used to compute conserved quantities (flux and density) for systems(More)
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