SLADI: a semi-Lagrangian alternating-direction implicit method for the numerical solution of advection-diffusion problems with application to electricity storage valuations

In this paper, an efficient and novel methodology for numerically solving advection-diffusion problems is presented: a semi-Lagrangian approach for hyperbolic problems of advection is combined with an alternating-direction implicit method for parabolic problems involving diffusion. This is used to value a four-dimensional "storage option" (linked to storing electricity) involving three space variables and time. Efficiency is obtained by solving (only) tridiagonal systems of equations at every time step by incorporating the alternating-direction methodology. Extensive numerical experimentation indicates that the method is stable and accurate; three variants of the scheme are assessed and excellent numerical convergence can be observed. Further, a methodology for determining and results for optimal storage operation are presented.