Numerical solutions of diffusion mathematical models with delay

Convergence of two implicit numerical schemes for diffusion mathematical models with delay

Diffusion equations with delay are basic mathematical models in areas where time lags or hereditary characteristics are present, as in the dynamics of structured populations, heat transfer in materials with thermal memory or control theory. In this work two implicit numerical difference schemes for the diffusion equations with delay ut(t, x) = a uxx(t, x) + a cuxx(t− τ , x), t > τ , 0 ≤ x ≤ l, ...

Analytic-numerical solutions of mixed problems for coupled systems of generalized diffusion equations with delay

REFERENCES [1] Wu, J. Theory and Application of Partial Functional Differential Equations. Springer Verlag, New York, 1996. [2] Martín, J.A., Rodríguez, F., Company, R. Analytical solution of mixed problems for the generalized diffusion equation with delay. Mathematical and Computer Modelling, 40 (2004), 361--369. [3] Reyes, E., Rodríguez, F., Martín, J.A. Cálculo eficiente de soluciones numéri...

Mathematical and Numerical Geohydrodynamic Models

Asymptotic and numerical solutions for diffusion models for compounded risk reserves with dividend payments

We study a family of diffusion models for compounded risk reserves, which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models which the dividend payments are paid from the risk reserves. After defining the process of conditional probability over finite time, the classical diffusion processes results turn the nonlinear stoc...

Numerical solutions for fractional reaction-diffusion equations

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...