“…For this notion of solution, Fast Fourier Transform (FFT) based methods have been proposed in [5,6] which are quite easy to implement, flexible and generic although they do not handle boundary conditions efficiently and are only applicable to linear problems with non space-dependent coefficients. Other possible notions of solution are viscosity solutions [7,8,9,10] to be approximated using finite difference methods and variational solutions [1,11,12] to be approximated using variational methods. In [13,14], important theoretical advances are presented to establish the connection between variational solutions and the corresponding expectations that European option prices represent.…”