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Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations

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Publicado en:Boundary Value Problems vol. 2025, no. 1 (Dec 2025), p. 7
Publicado:
Hindawi Limited
Materias:
Chebyshev approximation
Basis functions
Exact solutions
Algorithms
Mathematical analysis
Galerkin method
Polynomials
Effectiveness
Partial differential equations
Approximation
Numerical analysis
Methods
Boundary conditions
Boundary value problems
Acceso en línea:Citation/Abstract
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Resumen:This investigation discusses a numerical approach to solving the hyperbolic telegraph equation in both one and two dimensions. Applying the Galerkin method is the basis of this approach. We use appropriate combinations of third-kind modified shifted Chebyshev polynomials (3KMSCPs) as basis functions to transform the governing partial differential equations into a collection of algebraic equations. Through spectral Galerkin techniques, we establish the convergence error to demonstrate that our algorithm is more effective and efficient. Five examples are examined to verify the effectiveness and resilience of the applied method by comparing errors and illustrating the results. Our results show that the current numerical solutions align closely with exact solutions. The current algorithm is simple to set up and is better suited to solving certain difficult partial differential equations.
ISSN:1687-2762
1687-2770
DOI:10.1186/s13661-024-01987-4
Fuente:Advanced Technologies & Aerospace Database