This article examines the solution of the Cauchy problem for the multidimensional generalized Euler-Poisson-Darboux equation using the method of spherical means. A special approach is employed, based on the expansion of the solution function into a series of spherical harmonics. The article details this approach and proposes an algorithm for its implementation. Numerical experiment results are also presented, demonstrating the effectiveness of the proposed method. Overall, the article constitutes a significant contribution to the study of multidimensional Euler-Poisson-Darboux equations and may be of interest to specialists in mathematics and physics.

Euler-Poisson-Darboux equation, Cauchy problem, multidimensional generalization, method of spherical means, spherical harmonics, Fourier series, explicit solution, numerical modeling, solution stability, convergence, applications in physics, applications in mechanics, mathematical physics, partial differential equations, solution algorithm.

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