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- Luis M. Abia
- 2010

Separable Hamiltonian systems of differential equations have the form dp/dt = -dH/dq, dq/dt = dH/dp, with a Hamiltonian function H that satisfies H = T(p) + K(q) (T and V are respectively the kinetic and potential energies). We study the integration of these systems by means of partitioned Runge-Kutta methods, i.e., by means of methods where different… (More)

- Luis M. Abia, Oscar Angulo, Juan C. López-Marcos, M. A. López-Marcos
- Mathematical and Computer Modelling
- 2010

The proliferative behaviour at the stationary state of a cell population within a tumour cord has been described by a non-classical boundary value problem for a hyperbolic first order integro-partial differential equation [2]. The model was theoretically analyzed in [5], where sufficient conditions are given on the fraction of cells which enter… (More)

- Luis M. Abia, Oscar Angulo, Juan C. López-Marcos, M. A. López-Marcos
- Mathematical and Computer Modelling
- 2009

- Luis M. Abia, Jesús María Sanz Serna
- Computing
- 1990

A time-discrete pseudospectral algorithm is suggested for the numerical solution of a nonlinear third order equation arising in fluidization. The nonlinear stability and convergence of the new scheme are analyzed. Numerical comparisons with available finite-difference methods are also reported which clearly indicate the superiority of the new scheme. Zur… (More)

- Luis M. Abia, Juan C. López-Marcos
- Mathematical biosciences
- 1999

We formulate explicit second-order finite difference schemes for the numerical integration of non-linear age-dependent population models. These methods have been designed by means of a representation formula for the theoretical solution of the integro-differential equation joint with open quadrature formulae for the numerical approximation of non-local… (More)

— We consider a nonlinear partial differential équation ansing in fluidtzed bed modelhng which has been numencally studied by Christie and Ganser These authors found that apparently reasonable implicit numerical schemes turn out either to be unconditionally unstable or to perform well only if the time step is suitably large. We analyze this strange… (More)

- Luis M. Abia, Oscar Angulo, Juan C. López-Marcos, M. A. López-Marcos
- J. Computational Applied Mathematics
- 2014

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