An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation

Haifa Bin Jebreen; Yurilev Chalco Cano; Ioannis Dassios; Haifa Bin Jebreen; Yurilev Chalco Cano; Ioannis Dassios

doi:10.3934/math.2021080

AIMS Mathematics

2021, Volume 6, Issue 2: 1296-1308. doi: 10.3934/math.2021080

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Research article

An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation

1.
Department of mathematics, College of science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
Departamento de Matematica, Universidad de Tarapaca, casilla 7D, Arica, Chile
3.
AMPSAS, University College Dublin, Dublin 4, Ireland

Received: 22 August 2020 Accepted: 29 September 2020 Published: 16 November 2020
MSC : 35L20, 65M60, 65T60

We employ the multi-wavelet Galerkin method for the numerical solution of the telegraph equation with initial and boundary conditions. The problem becomes a sparse system of linear equations and the GMRES method is used to solve this system. The advantages of this scheme are complexity reduction, simplicity, and less grid selection. The convergence analysis is investigated and numerical experiments guarantee it. To show the ability of the method, we compare it with other methods and it can be confirmed that our results are better than others.
- hyperbolic equations,
- Galekin method,
- multi-wavelet
Citation: Haifa Bin Jebreen, Yurilev Chalco Cano, Ioannis Dassios. An efficient algorithm based on the multi-wavelet Galerkin method for telegraph equation[J]. AIMS Mathematics, 2021, 6(2): 1296-1308. doi: 10.3934/math.2021080

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Abstract

We employ the multi-wavelet Galerkin method for the numerical solution of the telegraph equation with initial and boundary conditions. The problem becomes a sparse system of linear equations and the GMRES method is used to solve this system. The advantages of this scheme are complexity reduction, simplicity, and less grid selection. The convergence analysis is investigated and numerical experiments guarantee it. To show the ability of the method, we compare it with other methods and it can be confirmed that our results are better than others.

References

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