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An RBF Based Finite Difference Method for the Numerical Approximation of Multi-term Nonlinear Time Fractional Two Dimensional Diffusion-Wave Equation

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Abstract

The main goal of this manuscript is to develop an RBF-based meshfree method to solve the multi-term time-fractional nonlinear two-dimensional diffusion-wave equation numerically. We discussed the present scheme’s stability analysis and theoretically proved that the scheme is convergent. Time fractional derivatives are defined in Caputo’s sense. Numerical examples on the regular and irregular domains with uniform and non-uniform points are given to validate the ability and accuracy of the developed scheme. The present results show that the proposed method is efficient and reliable for modeling and simulating the considered problems.

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  1. Department of Basic Sciences and Humanities, Rajiv Gandhi Institute of Petroleum Technology, Amethi, 229304, India

    Akanksha Bhardwaj & Alpesh Kumar

  2. Department of Mathematics, Indian Institute of Science Education and Research, Bhopal, India

    Awanish Kumar Tiwari

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Bhardwaj, A., Kumar, A. & Tiwari, A.K. An RBF Based Finite Difference Method for the Numerical Approximation of Multi-term Nonlinear Time Fractional Two Dimensional Diffusion-Wave Equation. Int. J. Appl. Comput. Math 8, 84 (2022). https://doi.org/10.1007/s40819-022-01270-z

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