Kuo Pen-Yu’s research while affiliated with Complutense University of Madrid and other places

... Historically, the problem of designing energy-conserving methods may date back to the decade of the 1970s [3,48]. However, it is worth mentioning that L. Vázquez and coauthors were probably the first researchers who pointed out the physical and mathematical significance of designing this type of schemes [43]. Various seminal papers by Vázquez and his coworkers were published in the 1990s, including various energy-conserving numerical schemes to solve partial differential equations like the Schrödinger equation [54], the sine-Gordon equation [6,19], Klein-Gordon equations [53], and even systems consisting of ordinary differential equations [20]. ...

Reference:

An implicit and convergent method for radially symmetric solutions of Higgs' boson equation in the de Sitter space-time

... Numerical method has become one of the important tools to derive the NLD solitary wave solutions, and to investigate their stability and interaction etc. The Crank-Nicolson (CN) scheme was first proposed for the 1D Soler model and used to simulate the interaction dynamics of the NLD solitary waves in [3,4]. Such interaction dynamics problem was carefully revisited in [39] by utilizing a fourth-order accurate RKDG method [40]. ...

Reference:

Three discontinuous Galerkin methods for one- and two-dimensional nonlinear Dirac equations with a scalar self-interaction