We consider Pennes’ bioheat equation and discuss an implicit numerical scheme which has better stability properties than other approaches. Our discussion concerns Carthesian geometry problems, however it carries over to spherical geometry models and more complicated shapes.

The phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.

W ostatnich latach obserwuje się wzrost znaczenia metod biologicznych, zarówno biomonitoringu jak i bioanalityki. Metody analityczne wykorzystujące materiał biologiczny stanowią coraz poważniejszą konkurencję dla klasycznych metod analitycznych.W obszarze metod bioanalitycznych na wyróżnienie zasługują testy biologiczne (biotesty). Konieczność wykonywania analiz wielu próbek środowiskowych w stosunkowo krótkim czasie doprowadziła...

The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by x˙ = − ∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.