High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region

R K Mohanty; Nikita Setia; Gunjan Khurana; Geetan Manchanda

doi:10.1016/j.mex.2022.101790

High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region

MethodsX. 2022 Jul 23:9:101790. doi: 10.1016/j.mex.2022.101790. eCollection 2022.

Authors

R K Mohanty¹, Nikita Setia², Gunjan Khurana³, Geetan Manchanda⁴

Affiliations

¹ Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India.
² Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi, 110017, India.
³ Department of Mathematics, I.P. College for Women, University of Delhi, Delhi, 110054, India.
⁴ Department of Mathematics, Maitreyi College, University of Delhi, Delhi, 110021, India.

Abstract

This article presents a new approximation of order four in exponential form for two-dimensional (2D) quasilinear partial differential equation (PDE) of elliptic form with solution domain being irrational. It is further extended for application to a system of quasilinear elliptic PDEs with Dirichlet boundary conditions (DBCs). The main highlights of the method framed in this article are as under:•It uses a 9-point stencil with unequal mesh to approach the solution. The error analysis is discussed to authenticate the order of convergence of the proposed numerical approximation.•Various validating problems, for instance the Burgers' equation, Poisson equation in cylindrical coordinates, Navier-Stokes (NS) equations in rectangular and cylindrical coordinates are solved using the proposed techniques to depict their stability. The proposed approximation produces solution free of oscillations for large values of Reynolds Number in the vicinity of a singularity.•The results of the proposed method are superior in comparison to the existing methods of [49] and [56].

Keywords: Burgers’ equation; Convergence analysis; Exponential form; Fourth order numerical approximation; Irrational domain with unequal mesh; Navier-Stokes equations; Quasilinear elliptic partial differential equation.