In this period, the dominant thrust was discretizing boundary-value problems and partial differential equations with careful attention to stability and convergence, especially for heat-conduction models and parabolic or elliptic equations. A cohesive computational paradigm formed around iterative relaxation techniques and linear-algebra solvers, combining relaxation theory, determinant-based analysis, and functional-iteration methods into a unified numerical workflow. Interpolation and multivariable approximation also matured, bridging one- and multi-variable problems through Lagrange-type strategies and conjugate-point ideas, and supporting broader numerical representations in physical contexts. Influential Works: The Crank–Nicolson time-stepping scheme for heat-type partial differential equations delivered second-order accuracy with unconditional stability and became a standard in computational practice. The nonlinear least-squares algorithm combining Gauss-Newton with adaptive damping established robust convergence for challenging models and wide applicability to parameter estimation. Foundational developments in Monte Carlo methods and iterative eigenvalue solvers for linear operators introduced transformative tools that shaped numerical analysis and large-scale computations in physics and engineering.