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- Title
High-precision numerical method for 1D quasilinear hyperbolic equations on a time-graded mesh: application to Telegraph model equation.
- Authors
Mohanty, R. K.; Ghosh, Bishnu Pada; Khurana, Gunjan
- Abstract
We study a new 3-level implicit numerical method of order 4 in space and 2 in time on a graded mesh in time for the solution of 1D quasilinear hyperbolic equation ztt = a(t, x, z)zxx + R(t, x, z, zt, zx), 0 < x < 1, 0 < t < T with associated Dirichlet boundary and initial conditions. Applying the proposed approximation to Telegraph model equation, we have established unconditional stability on a time-graded mesh. Linear difference schemes are solved by direct methods, that is, using a tri-diagonal solver and Newton–Raphson iterative method employed to handle nonlinear difference equations at each advanced time level. An order two in time explicit scheme at first time level is derived, which can be used in the proposed approximation while computing. Seven important benchmark problems are computed to validate the utility of the proposed 3-level implicit approximation.
- Subjects
NONLINEAR difference equations; HYPERBOLIC differential equations; TELEGRAPH &; telegraphy; NEWTON-Raphson method; BENCHMARK problems (Computer science); NONLINEAR wave equations
- Publication
Soft Computing - A Fusion of Foundations, Methodologies & Applications, 2023, Vol 27, Issue 10, p6095
- ISSN
1432-7643
- Publication type
Article
- DOI
10.1007/s00500-023-07909-3