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NSFD schemes for a class of nonlinear generalised advection–diffusion–reaction equation

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Abstract

This paper deals with the nonlinear generalised advection–diffusion–reaction (GADR) equation subject to some initial and boundary conditions (BCs). Some exact finite difference (EFD) schemes and non-standard finite difference (NSFD) schemes are derived. Positivity and boundedness of the proposed NSFD schemes are analysed analytically and numerically. Theoretical results are very well supported by solved examples. The major achievements of NSFD schemes are that they give highly accurate solutions for very few spatial and temporal divisions.

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Authors and Affiliations

  1. School of Advanced Sciences & Language, Vellore Institute of Technology Bhopal University, Bhopal, 466114, India

    SHEERIN KAYENAT

  2. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801106, India

    AMIT K VERMA

Authors
  1. SHEERIN KAYENAT
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  2. AMIT K VERMA
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Correspondence to AMIT K VERMA.

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KAYENAT, S., VERMA, A.K. NSFD schemes for a class of nonlinear generalised advection–diffusion–reaction equation. Pramana - J Phys 96, 14 (2022). https://doi.org/10.1007/s12043-021-02239-1

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  • DOI: https://doi.org/10.1007/s12043-021-02239-1

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