Fractals· 2026Q1
A COMPUTATIONAL ALGORITHM FOR THE NUMERICAL SOLUTION OF TWO-DIMENSIONAL TELEGRAPH INTERFACE PROBLEMS
- 0citations
- Q1SCImago
- 2026year
Short summary
A novel hybrid Haar wavelet and finite difference algorithm accurately solves 2D telegraph interface problems, handling both linear and nonlinear cases with sharp transitions.
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Key points
- Hybrid Haar wavelet and finite difference method for 2D telegraph interface problems.
- Handles both linear (Gauss elimination) and nonlinear (Newton's quasi-linearization) cases.
- Accurate and stable even with sharp transitions and discontinuities.
- Performance evaluated using maximum absolute errors, RMS errors, and convergence rates.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper introduces the hyperbolic two-dimensional telegraph interface model with regular interfaces, employing a hybrid numerical technique that combines Haar wavelets and the finite difference method for both linear and nonlinear problems. Spatial derivatives are approximated using truncated Haar wavelet series, while time derivatives are managed via the finite difference method. For linear problems, the Gauss elimination technique is used to solve the resulting algebraic system, whereas Newton’s quasi-linearization technique addresses nonlinearity in nonlinear problems. Performance metrics, the computation of maximum absolute errors, root mean square errors, and computational convergence rates is carried out for various configurations of collocation points demonstrating the method’s stability and accuracy, even with sharp transitions or discontinuities. Numerical experiments and analysis confirm the method’s broad applicability and precision.
The authors' abstract, as published at the source. Fractals, 2026 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics