UPPSALATOR

Example of 1-D pde solver for a nonlinear integro-differential Dirichlet problem

UPPSALATOR is an electroosmotical oscilLATOR developed in UPPSALA by T. Teorell. Up to now oscillations were observed only at constant currrent. Oscillations at constant
voltage were considered earlier as impossible. This program demonstrates the UPPSALATOR at any constant voltage.
It solves nonlinear integro-differential Dirichlet problem C(T,X)=?, 0<T (time),
0<=X<=1 (1-D space).

Equation of convective diffusion for C(T,X):

pi^2*dCdT=d2CdX2-V(T)*dCdX

dCdT and dCdX are time and space derivatives of C respectively, d2CdX2 is the second spatial derivative.

C(T,0)=CLEF; 0<=CLEF<1
C(T,1)= 1;

Arbitrary initial condition, here
C(0,X)=linspace(CLEF,1,N),
N = mesh size (odd integer, def. 23)

V= -P(T) + VOLT*F(T) (V = Velocity)
VOLT > 0 = constant voltage;
P = pressure (a dynamical variable :-)

dPdT=lambda*V;

lambda > 0 empirical constant (here 0.2)

F(T) = electroosmotical factor, earlier considered as a constant.

F(T)=integral(0,1,1/C(T,X)^1.5 dX)/...
integral(0,1,1/C(T,X) dX);