18/02/2010, 15:00 — 16:00 — Sala P1, Pavilhão de Matemática
Filomena Teodoro, CEMAT and Instituto Politécnico de Setúbal
Numerical Approximation of a Nonlinear Mixed Type Functional
Differential Equation
We begin with a brief review of our previous work with
autonomous and non-autonomous linear MTFDEs using collocation,
least squares and finite element methods. Then we focus on the
approximate solution of a nonlinear mixed type functional
differential equation (MTFDE) arising from nerve conduction theory.
The considered model describes the conduction of neuroelectric
signals in a myelinated nerve axon (composed by a membrane and
nodes) . In this case, when the membrane is depolarized at a node,
the myelin tends not to depolarize the adjacent region of membrane,
but instead it appears to jump to the next node to excite the
membrane there, as described by the authors of [1]. As a
consequence, the variation in time of the electric potential at
each node depends on the electric potential of the neighbour nodes
and is modeled by a first order nonlinear functional differential
equation with deviated arguments. Following the approach introduced
previously for linear MTFDEs, we propose and analyse a new
computational method for the solution of this problem.
References
- H. Chi, J.Bell and B. Hassard, Numerical solution of a
nonlinear advance-delay-differential equation from nerve conduction
theory, J.Math.Biology, 24 (1986), 583-601.
