A compact high resolution semi-variable mesh exponential finite difference method for non-linear boundary value problems of elliptic nature

Volume 33, Issue 1, pp 87--107 http://dx.doi.org/10.22436/jmcs.033.01.07

Publication Date: November 26, 2023 Submission Date: September 23, 2022 Revision Date: August 02, 2023 Accteptance Date: October 18, 2023

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Authors

G. Manchanda - Department of Mathematics, Maitreyi College, University of Delhi, Delhi 110021, India.

Abstract

In this research an original exponential approximation of second accuracy in \(y\)- and third accuracy in \(x\)-axis employing full step discretization has been designed for solving 2D non-linear partial differential equation of elliptic nature in a rectangular domain. We adopted non-constant grid spacing in \(x\)-axis and constant grid spacing in \(y\)-axis in numerical computation of convection-diffusion equation where convection term dominates. An exhaustive error behaviour of the technique has been analysed. Non-linear elliptic equations are computed using this method. Lastly, proposed idea is scrutinized on simulations of physical repute with emphasis on convection-diffusion equation articulating the efficacy of the technique.

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Keywords

• Quasilinear elliptic equations
• full-step
• exponential estimation
• error estimate
• Burger's equation
• convection-diffusion equation
• Navier-Stokes equations
• multi-harmonic

MSC

•  65M06
•  65M12
•  65M22
•  65N06
•  65N12

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