I will identify several applications of numerical analysis in the gas
kinetic theory and general relativity that have emerged
recently. These problems continue to puzzle physicists and engineers,
however, they have not been rigorously studied yet. In fact,
formulations of the problems are available, however, their solutions
are expected to be involved and require the development of new
analytic techniques. In the conclusion, we anticipate the development
of a new generation of numerical methods or a considerable
modification of the existing one to address the challenges.