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Design and analysis of a computational procedure for a class of time fractional multi-term diffusion problem

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

The numerical solution of the time fractional multi-term diffusion problem is achieved in this study by utilizing the spline collocation method. This equation is useful in the study of mechanical wave propagation in viscoelastic media, transport in amorphous semiconductors, and non-Markovian diffusion processes with memory. The collocation approach uses the spline basis function for space integration and a weighted finite difference strategy for temporal domain integration. The technique’s stability is examined using the von Neumann scheme, and it is determined to be unconditionally stable. The suggested approach is determined to be fourth-order convergent in space for a specific choice of parameters and \((2-\beta )\) order convergent in time. We provide some numerical examples to support our theoretical approach. The numerical order of convergence matches the theoretical order completely. The \(L_{2}\) errors are computed, and the results are compared to earlier works.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Kurukshetra, Kurukshetra, Haryana, 136119, India

    A. S. V. Ravi Kanth & S. Deepika

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  1. A. S. V. Ravi Kanth
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  2. S. Deepika
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Correspondence to A. S. V. Ravi Kanth.

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Kanth, A.S.V.R., Deepika, S. Design and analysis of a computational procedure for a class of time fractional multi-term diffusion problem. Soft Comput 27, 1241–1263 (2023). https://doi.org/10.1007/s00500-022-07717-1

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