  In this study, we conduct a thorough and meticulous examination of the Runge
phenomenon. Initially, we engage in an extensive review of relevant literature,
which aids in delineating the genesis and essence of the Runge phenomenon,
along with an exploration of both conventional and contemporary algorithmic
solutions. Subsequently, the paper delves into a diverse array of resolution
methodologies, encompassing classical numerical approaches, regularization
techniques, mock-Chebyshev interpolation, the TISI (Three-Interval
Interpolation Strategy), external pseudo-constraint interpolation, and
interpolation strategies predicated upon Singular Value Decomposition (SVD).
  For each method, we not only introduce but also innovate a novel algorithm to
effectively address the phenomenon. This paper executes detailed numerical
computations for each method, employing visualization techniques to vividly
illustrate the efficacy of various strategies in mitigating the Runge
phenomenon. Our findings reveal that although traditional methods exhibit
commendable performance in certain instances, novel approaches such as
mock-Chebyshev interpolation and regularization-centric methods demonstrate
marked superiority in specific contexts.
  Moreover, the paper provides a critical analysis of these methodologies,
specifically highlighting the constraints and potential avenues for enhancement
in SVD decomposition-based interpolation strategies. In conclusion, we propose
future research trajectories and underscore the imperative of further
exploration into interpolation strategies, with an emphasis on their practical
application validation. This article serves not only as a comprehensive
resource on the Runge phenomenon for researchers but also offers pragmatic
guidance for resolving real-world interpolation challenges.
