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Search: authors:"Robert A. Van Gorder"

6 papers found.
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Exact solution to a generalized model for compact stars

Recent work based on an approximation method suggested some odd behaviors may be possible in solutions to a generalized model for compact stars. We show that it was the error in these approximations and error coming from non-physical boundary conditions which lead to the odd behavior. As it turns out, the generalized model for compact stars actually admits an exact solution, and we ...

On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method (HAM). In the present paper, we demonstrate that such a view is only valid in very special cases, and in general, the HAM is far more robust. In particular, ...

Reduction of dimension for nonlinear dynamical systems

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where this reduction is possible, we employ differential elimination ...

Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation

Robert A. Van Gorder 0 1 0 Subject Index: 010, 030 1 Department of Mathematics, University of Central Florida , Orlando, FL 32816-1364, USA We consider a method of obtaining exact implicit relations