Pseudospectral Roaming Contour Integral Methods for Convection-Diffusion Equations

Abstract We generalize ideas in the recent literature and develop new ones order to propose a general class of contour integral methods for linear convection–diffusion PDEs particular those arising finance. These aim provide numerical approximation solution by computing its inverse Laplace transform. The choice integration is determined computation few suitably weighted pseudo-spectral level sets leading operator equation. Parabolic hyperbolic profiles proposed are investigated compared elliptic originally Guglielmi, López-Fernández Nino 2020, see Guglielmi et al. (Math Comput 89:1161–1191, 2020). In summary, article provides comparison among three different profiles; proposes fast pseudospectral roaming method; optimizes selection time windows on which one may arbitrarily approximate no extra computational cost with respect case fixed instant; focuses extensively aspects it reference MATLAB code [20], where all algorithms described here implemented.