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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| 出版年: | Boundary Value Problems vol. 2025, no. 1 (Dec 2025), p. 7 |
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| 出版事項: |
Hindawi Limited
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| 主題: | |
| オンライン･アクセス: | Citation/Abstract Full Text - PDF |
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MARC
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| 245 | 1 | |a Spectral framework using modified shifted Chebyshev polynomials of the third-kind for numerical solutions of one- and two-dimensional hyperbolic telegraph equations | |
| 260 | |b Hindawi Limited |c Dec 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a 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. | |
| 653 | |a Chebyshev approximation | ||
| 653 | |a Basis functions | ||
| 653 | |a Exact solutions | ||
| 653 | |a Algorithms | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Galerkin method | ||
| 653 | |a Polynomials | ||
| 653 | |a Effectiveness | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Approximation | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Methods | ||
| 653 | |a Boundary conditions | ||
| 653 | |a Boundary value problems | ||
| 773 | 0 | |t Boundary Value Problems |g vol. 2025, no. 1 (Dec 2025), p. 7 | |
| 786 | 0 | |d ProQuest |t Advanced Technologies & Aerospace Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3156307742/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3156307742/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |