The field of numerical methods for differential equations and integral equations is witnessing significant developments, with a focus on improving the accuracy and efficiency of existing methods. Recent research has been directed towards the development of new techniques for solving fractional differential equations, Volterra integral equations, and parametric differential equations. The use of neural networks and machine learning approaches is becoming increasingly popular in this area, with applications in ocean forecasting, climate modeling, and other fields. Noteworthy papers include:

• Generalizable Implicit Neural Representations via Parameterized Latent Dynamics for Baroclinic Ocean Forecasting, which presents a novel framework for efficient and accurate ocean forecasting.
• Spectral coefficient learning physics informed neural network for time-dependent fractional parametric differential problems, which introduces a new scientific machine learning approach for solving parametric time-fractional differential equations.
• A numerical Bernstein splines approach for nonlinear initial value problems with Hilfer fractional derivative, which proposes a numerical method for approximating solutions to generalized nonlinear initial value problems with Hilfer fractional derivatives.