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High-resolution half-step compact numerical approximation for 2D quasilinear elliptic equations in vector form and the estimates of normal derivatives on an irrational domain
- Source :
- Soft Computing. 25:9967-9991
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- This paper describes a novel implicit fourth-order approximation for solving the 2D quasilinear elliptic partial differential equations on an irrational domain. In this technique, we use 9-grid points compact cell with half-step unequal mesh discretization in both x- and y-coordinates. We also study fourth-order explicit approximations for the solution of normal derivatives on an irrational domain. The proposed method has been extended to solve quasilinear elliptic equations in vector form. Stability analysis is discussed in order to verify the convergence of the proposed computational method. On applications, we solve several benchmark nonlinear elliptic problems including steady-state Burgers’ and Navier–Stokes equations. The outcome of numerical results is shown the reliability, accuracy and the stability character of the method even for high values of Re.
- Subjects :
- 0209 industrial biotechnology
Discretization
02 engineering and technology
Stability (probability)
Domain (mathematical analysis)
Theoretical Computer Science
Nonlinear system
020901 industrial engineering & automation
Elliptic partial differential equation
Irrational number
Convergence (routing)
0202 electrical engineering, electronic engineering, information engineering
Benchmark (computing)
Applied mathematics
020201 artificial intelligence & image processing
Geometry and Topology
Software
Mathematics
Subjects
Details
- ISSN :
- 14337479 and 14327643
- Volume :
- 25
- Database :
- OpenAIRE
- Journal :
- Soft Computing
- Accession number :
- edsair.doi...........a6c11387c5b795927075b76134be30ba
- Full Text :
- https://doi.org/10.1007/s00500-020-05505-3