Paul Warne

 

Professor, Applied Mathematics
warnepg@jmu.edu
Contact Info
Website: http://educ.jmu.edu/~warnepg/

 

Research Description

The spectrum of my research includes highly accurate numerical solution of systems of ordinary and partial differential equations that arise naturally and are vital to both the sciences and engineering; the theoretical modeling of nonlinear elastic deformations important to the field of nonlinear solid mechanics; and the study and development of an eight dimensional Grassmann and Clifford algebra that utilizes hyper-complex numbers to extend the geometric concept of the Hamiltonian vector to higher dimensions.

Education
  • PhD in Applied Mathematics, 1993, University of Virginia, Charlottesville, VA
  • MS in Mathematics, 1998, James Madison University
  • BA in Studio Art, 1984, Ashland University, Ashland, OH
Select Publications
  • Warne, P.G, and Warne D.A. (2016) Torsion in nonlinearly elastic incompressible circular cylinders, International Journal of Non-linear Mechanics, 88, 158-166.
  • Thelwell, R.J., Warne, P.G, and Warne D.A. (2012) Cauchy-Kowalevski and Polynomial Ordinary Differential Equations, Electron. J. Diff. Equ., 11, 1-8.
  • Warne D.A., and Warne, P.G. (2011) “Must Tensor Addition be among Same-Order Tensors?”, Mathematics and Mechanics of Solids, 16, 769-777.

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