Capturing Discontinuities with Precision: A Numerical Exploration of 3D Telegraph Interface Models via Multi-Resolution Technique
This study presents a hyperbolic three-dimensional telegraph interface model with regular interfaces, numerically solved using a hybrid scheme that integrates Haar wavelets and the finite difference method. Spatial derivatives are approximated via a truncated Haar wavelet series, while temporal deri...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2391 |
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| Summary: | This study presents a hyperbolic three-dimensional telegraph interface model with regular interfaces, numerically solved using a hybrid scheme that integrates Haar wavelets and the finite difference method. Spatial derivatives are approximated via a truncated Haar wavelet series, while temporal derivatives are discretized using the finite difference method. For linear problems, the resulting algebraic system is solved using Gauss elimination; for nonlinear problems, Newton’s quasi-linearization technique is applied. The method’s accuracy and stability are evaluated through key performance metrics, including the maximum absolute error, root mean square error, and the computational convergence rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mi>c</mi></msub><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, across various collocation point configurations. The numerical results confirm the proposed method’s efficiency, robustness, and capability to resolve sharp gradients and discontinuities with high precision. |
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| ISSN: | 2227-7390 |