Spectral methods in MatLab
Exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
Mathematical Methods in Optimization of Differential Systems
Mathematical Methods in Optimization of Differential Systems
Exponential time differencing for stiff systems
Journal of Computational Physics
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
"It was an artefact not the result": A note on systems dynamic model development tools
Environmental Modelling & Software
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In this paper we study a prey-predator model defined by an initial-boundary value problem whose dynamics is described by a Holling type III functional response. We establish global existence and uniqueness of the strong solution. We prove that if the initial data are positive and satisfy a certain regularity condition, the solution of the problem is positive and bounded on the domain Q=(0,T)x@W and then we deduce the continuous dependence on the initial data. A numerical approximation of the system is carried out with a spectral method coupled with the fourth-order Runge-Kutta time solver. The biological relevance of the comparative numerical results is also presented.