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An efficient numerical algorithm for the study of time fractional Tricomi and Keldysh type equations

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Abstract

This work addresses a hybrid scheme for the numerical solutions of time fractional Tricomi and Keldysh type equations. In proposed methodology, Haar wavelets are used for discretization in space while \(\theta\)-weighted scheme coupled with second order finite differences and quadrature rule are employed for temporal discretization and fractional derivative respectively. Stability of the proposed scheme is described theoretically and validated computationally which is an essential chunk of the current work. Efficiency of the suggested scheme is endorsed through resolutions level and time step size. Goodness of the obtained solutions confirmed through computing error norms \({\mathbb E}_{\infty }\), \({\mathbb E}_2\) and matching with existing results in literature. Moreover, convergence rate is also checked for considered problems. Numerical simulations show good performance for both 1D and 2D test problems.

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Authors and Affiliations

  1. Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KP, 26000, Pakistan

    Abdul Ghafoor & Amir Rasool

  2. Faculty of Engineering Sciences, GIK Institute, Topi, KP, 23640, Pakistan

    Sirajul Haq

  3. Department of Mathematics, Cankaya University, 06530, Balgat, Ankara, Turkey

    Dumitru Baleanu

  4. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Abdul Ghafoor
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  2. Sirajul Haq
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  3. Amir Rasool
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  4. Dumitru Baleanu
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Correspondence to Abdul Ghafoor.

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Ghafoor, A., Haq, S., Rasool, A. et al. An efficient numerical algorithm for the study of time fractional Tricomi and Keldysh type equations. Engineering with Computers 38, 3185–3195 (2022). https://doi.org/10.1007/s00366-020-01257-8

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  • DOI: https://doi.org/10.1007/s00366-020-01257-8

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