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Modelling of multicomponent diffusive phase transformation in solids

Vala, Jiří (2008)

Programs and Algorithms of Numerical Mathematics

Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases ( α , γ ) and in moving interface of finite thickness ( β ), in whose center the ideal liquid material behaviour can be detected....

Numerical approximation of density dependent diffusion in age-structured population dynamics

Gerardo-Giorda, Luca (2013)

Applications of Mathematics 2013

We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona (2008)

Programs and Algorithms of Numerical Mathematics

We consider functionals of a potential energy ℙ ψ ( u ) corresponding to 𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 . We are dealing with 𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒 with 𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 . Various types of the subsoil of the plate are described by various types of the 𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒 nonlinear term ψ ( u ) . The aim of the paper is to find a suitable computational algorithm.

Currently displaying 161 – 180 of 362