Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 9 2 2025 11 12 Analytical and Numerical Approaches to Nonlinear Equations in Holographic Black Hole Backgrounds 287 294 1953 10.22128/ansne.2025.3061.1155 EN Behnam Pourhassan Canadian Quantum Research Center, 204-3002 32 Ave, Vernon, Canada 0000-0003-1338-7083 Journal Article 2025 09 17 We investigate nonlinear differential equations arising in holographic models of black hole spacetimes within the AdS/CFT correspondence. Emphasis is placed on analytical approximations and numerical solutions of scalar perturbations and nonlinear wave equations in asymptotically anti-de Sitter black holes. We show how effective potentials lead to boundary value problems governed by nonlinear ordinary differential equations. Analytical methods, such as matched asymptotic expansions and perturbative ans"{a}tze, are compared with spectral numerical approaches. Applications to holographic thermalization, quasinormal spectra, and cosmological analogues are discussed. Our results highlight the interplay between nonlinear analysis and physical interpretation in string-inspired models of gravity. https://ansne.du.ac.ir/article_1953_454a3bcbe83645fbf25b0693be877bfc.pdf