Mohanty R K, Setia Nikita, Khurana Gunjan, Manchanda Geetan
Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India.
Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi, 110017, India.
MethodsX. 2022 Jul 23;9:101790. doi: 10.1016/j.mex.2022.101790. eCollection 2022.
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].
本文提出了一种指数形式的四阶新近似方法，用于求解解域为无理数的二维（2D）椭圆型拟线性偏微分方程（PDE）。该方法进一步扩展应用于具有狄利克雷边界条件（DBCs）的拟线性椭圆型偏微分方程组。本文所构建方法的主要亮点如下：
• 它使用具有不等网格的九点模板来逼近解。讨论了误差分析以验证所提出数值近似的收敛阶。
• 使用所提出的技术求解各种验证问题，例如伯格斯方程、圆柱坐标下的泊松方程、直角坐标和圆柱坐标下的纳维 - 斯托克斯（NS）方程，以描述其稳定性。对于奇点附近雷诺数的大值，所提出的近似产生无振荡的解。
• 与[49]和[56]的现有方法相比，所提出方法的结果更优。
