Finite volume difference scheme for a transformed stationary air pollution problem

A new approach is proposed for the numerical solution of boundary value onedimensional problem of advection-diffusion equation, which arise, among others, in air pollution modeling. Since the problem is posed in unbounded interval we use a log-transformation to confine the computational region. We derive a finite volume scheme and show that it is monotone, i.e it preserves the nonnegativity property. Numerical experiments show higher accuracy of our scheme near the degenerate boundary and the Dirac-delta source term.