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Abstract
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Fourth-order Emden-Fowler equations are used to model phenomena with highly nonlinear behavior and singularities in a number of applied sciences, such as astrophysics, fluid mechanics, thermal conduction, and nonlinear elasticity. Because of their fourth-order and nonlinear characteristics, analytical solutions are typically very challenging or impossible. Particularly when dealing with singularities or complicated boundary conditions, traditional numerical methods usually encounter difficulties like instability, slow convergence, and low accuracy. The need for effective and dependable numerical methods that can faithfully represent the behavior of the solution while preserving computational viability is thus highlighted. Newton-Raphson iteration in conjunction with semi-orthogonal B-spline wavelets creates a strong framework that offers high-order approximation, local refinement capabilities, and efficient nonlinearity handling. This research is important because it will help solve fourth-order Emden-Fowler equations in a precise, stable, and computationally efficient manner, which will advance theoretical research as well as real-world applications in applied mathematics and engineering.
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