Robert A. Van Gorder, University of Central Florida


Analytical and numerical solutions to some nonlinear differential equations


Abstract: We consider three different nonlinear dierential equations, for which we obtain a variety of analytical and numerical solutions. In particular, we consider (i) traveling wave solutions to the density dependent diffusion Nagumo equation u_t = (u^m u_x)_x + u(1-u)(u-α), (ii) solutions to the Lane Emden y"(x)+(2/x)y'(x)+y^M(x) via the homotopy analysis method, and (iii) solutionsto the Brinkman-Forchheimer momentum equation Δu-Au₂-Bu+C = 0 for a unidirectional flow over a rectangular domain via the Rayleigh-Ritz method.

Advisor: K. Vajravelu (UCF)

References:

R. A. Van Gorder and K. Vajravelu, Analytical and numerical solutions of the density dependent diffusion Nagumo equation, Physics Letters A, 372 31 (2008) 5152-5158.
R. A. Van Gorder and K. Vajravelu, Analytic and Numerical Solutions to theLane-Emden Equation, Physics Letters A, 372 39 (2008) 6060-6065.
R. A. Van Gorder, K. Vajravelu, and F.T. Akyildiz, Solutions to the Brinkman-Forchheimer momentum equation for a unidirectional flow over a rectangular domain, International Journal of Fluid Mechanics Research, accepted (2008).