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In this study, we employed the homotopy analysis transform method (HATM) to derive an iterative scheme to numerically solve a singular second-order hyperbolic pseudo-differential equation. We evaluated the effectiveness of the derived scheme in solving both linear and nonlinear equations of similar nature through a series of illustrative examples. The stability of this scheme in handling the approximate solutions of these examples was studied graphically and numerically. A comparative analysis with existing methodologies from the literature was conducted to assess the performance of the proposed approach. Our findings demonstrate that the HATM-based method offers notable efficiency, accuracy, and ease of implementation when compared to the alternative technique considered in this study. [ABSTRACT FROM AUTHOR]

In this article, we present a numerical iterative scheme for solving a non-local singular initial-boundary value problem by combining two well known efficient methods. Namely, the homotopy analysis method and the double Laplace transform method. The resulting scheme is tested on a set of test examples to illustrate its efficiency, it generates the exact analytical solution for each one of these examples. The convergence of the resulting numerical solutions of these examples is tested both graphically and numerically. [ABSTRACT FROM AUTHOR]