The field of numerical methods for financial derivatives and Lie group splines is witnessing significant advancements. Researchers are exploring innovative approaches to solve complex equations, such as the time-fractional Black-Scholes equation, using modified cubic B-spline based differential quadrature methods and multinode Shepard collocation methods. These methods exhibit high-order convergence and accuracy, making them promising tools for financial modeling. Additionally, the development of product of exponentials (POE) splines on Lie groups is enabling more effective interpolation and approximation of curves on these groups. Noteworthy papers include:

• A paper on modified cubic B-spline based differential quadrature methods, which demonstrates a fourth-order convergence in the space direction and the order 2-alpha in time.
• A paper on product of exponentials (POE) splines on Lie groups, which introduces a new approach to construct splines on these groups and allows for local curves between arbitrary points.