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This paper presents a unified hyperbolic system that integrates advection and diffusion into a single framework by extending the first-order system approach. The proposed method allows for the development of numerical schemes that achieve rapid convergence, O(h) time steps, and simultaneous computation of solution gradients, demonstrating significant computational advantages over traditional methods. Numerical results validate the effectiveness of this approach in one and two-dimensional boundary-layer prob

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11faizalakbar.s

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EN