The numerical calculation of traveling wave solutions of nonlinar parabolic equations
SIAM Journal on Scientific and Statistical Computing
Comment on the discrete ordinate method in the kinetic theory of gases
Journal of Computational Physics
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
A moving collocation method for solving time dependent partial differential equations
Applied Numerical Mathematics
Journal of Computational Physics
Numerical solution of Fisher's equation using a moving mesh method
Journal of Computational Physics
Stability of Moving Mesh Systems of Partial Differential Equations
SIAM Journal on Scientific Computing
On traveling wave solutions of Fisher's equation in two spatial dimensions
SIAM Journal on Applied Mathematics
Improving the accuracy of the matrix differentiation method for arbitrary collocation points
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
A direct spectral collocation Poisson solver in polar and cylindrical coordinates
Journal of Computational Physics
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Computational solution of two-dimensional unsteady PDEs using moving mesh methods
Journal of Computational Physics
Delay induced traveling wave fronts in reaction diffusion equations of KPP-Fisher type
Journal of Computational and Applied Mathematics
Spectral Differencing with a Twist
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A multidomain spectral method for supersonic reactive flows
Journal of Computational Physics
Mathematical and Computer Modelling: An International Journal
Pseudospectral method of solution of the Fitzhugh-Nagumo equation
Mathematics and Computers in Simulation
The spectral methods for parabolic Volterra integro-differential equations
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
In this paper, we develop an accurate and efficient pseudospectral solution of Fisher's equation, a prototypical reaction-diffusion equation. The solutions of Fisher's equation are characterized by propagating fronts that can be very steep for large values of the reaction rate coefficient. There is an ongoing effort to better adapt pseudospectral methods to the solution of differential equations with solutions that resemble shock waves or fronts typical of hyperbolic partial differential equations. The collocation method employed is based on Chebyshev-Gauss-Lobatto quadrature points. We compare results for a single domain as well as for a subdivision of the main domain into subintervals. Instabilities that occur in the numerical solution for a single domain, analogous to those found by others, are attributed to round-off errors arising from numerical features of the discrete second derivative matrix operator. However, accurate stable solutions of Fisher's equation are obtained with a multidomain pseudospectral method. A detailed comparison of the present approach with the use of the sine interpolation is also carried out.