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High-resolution compact numerical method for the system of 2D quasi-linear elliptic boundary value problems and the solution of normal derivatives on an irrational domain with engineering applications

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Abstract

In this paper, we present a novel approach to attain fourth-order approximate solution of 2D quasi-linear elliptic partial differential equation on an irrational domain. In this approach, we use nine grid points with dissimilar mesh in a single compact cell. We also discuss appropriate fourth-order numerical methods for the solution of the normal derivatives on a dissimilar mesh. The method has been protracted for solving system of quasi-linear elliptic equations. The convergence analysis is discussed to authenticate the proposed numerical approximation. On engineering applications, we solve various test problems, such as linear convection–diffusion equation, Burgers’equation, Poisson equation in singular form, NS equations, bi- and tri-harmonic equations and quasi-linear elliptic equations to show the efficiency and accuracy of the proposed methods. A comprehensive comparative computational experiment shows the accuracy, reliability and credibility of the proposed computational approach.

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Acknowledgements

The authors thank the reviewers for their valuable suggestions, which substantially improved the quality of the paper.

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Authors and Affiliations

  1. Department of Electrical and Computer Science, University of Delaware, Newark, DE, 19716, USA

    Ishaani Priyadarshini

  2. Department of Applied Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India

    R. K. Mohanty

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  1. Ishaani Priyadarshini
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  2. R. K. Mohanty
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Correspondence to R. K. Mohanty.

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Priyadarshini, I., Mohanty, R.K. High-resolution compact numerical method for the system of 2D quasi-linear elliptic boundary value problems and the solution of normal derivatives on an irrational domain with engineering applications. Engineering with Computers 38 (Suppl 1), 539–560 (2022). https://doi.org/10.1007/s00366-020-01150-4

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  • DOI: https://doi.org/10.1007/s00366-020-01150-4

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