Numerical valuation of options with jumps in the underlying

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Robust numerical valuation of European and American options under the CGMY process (2007, methodology): “In [13, 18], an integration by parts technique was used to transform the integral part into a weakly singular Volterra equation.”
Robust numerical methods for contingent claims under jump diffusion processes (2005, result): “Note that we have recently become aware of a paper (Vazquez and Oosterlee, 2003) which is similar in spirit to the methods suggested in this work, although the details of the implementation differ.”
An iterative method for pricing American options under jump-diffusion models (2011, methodology): “We adopt the formulation presented by Almendral and Oosterlee in [2], where the matrix B is split with a regular splitting B = T − J , where T = I + θk∆tkD and J = −θk∆tkR.”
Numerical solution of two asset jump diffusion models for option valuation (2008, methodology): “A similar approach, which uses an iterative method to solve the implicit discretized PIDE and which also uses an FFT to carry out the dense matrix-vector multiply, was developed by Almendral and Oosterlee [2].”