NUMERICAL SOLUTION OF HYPERBOLIC GOURSAT PARTIAL DIFFERENTIAL EQUATIONS WITH HYBRID CENTRAL DIFFERENCE - TAYLOR SERIES EXPANSIONS METHOD

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Abstract
This paper investigates a new method for solving the Goursat partial differential equation (PDE) using a combination of the central finite difference method (FDM) and Taylor series expansion. The study evaluates the effectiveness and accuracy of this new approach, analyzing linear Goursat problems and conducting multiple numerical experiments. The simulation study demonstrates that the suggested approach surpasses the existing method in terms of performance and accuracy. Applying this proposed scheme will minimize the cost, especially for engineers that might apply this model in solving their real-life problems.