A new fourth order discretization for singularly perturbed two dimensional nonlinear elliptic boundary value problems
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Publication:2493717
DOI10.1016/j.amc.2005.08.023zbMath1093.65103OpenAlexW2048986883MaRDI QIDQ2493717
Swarn Singh, Ranjan Kumar Mohanty
Publication date: 16 June 2006
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2005.08.023
numerical resultssingular perturbationerror estimatesnonlinear elliptic equationdifference methoddiffusion-convection equationnormal derivativescylindrical polar coordinatesarithmetic average discretization
Nonlinear boundary value problems for linear elliptic equations (35J65) Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Single cell discretizations of order two and four for biharmonic problems
- Analysis of a fourth-order compact scheme for convection-diffusion
- Order \(h^ 4\) difference methods for a class of singular two space elliptic boundary value problems
- Convergence of iterative methods for a fourth-order discretization scheme
- Poisson equation solver with fourth-order accuracy by using interpolated differential operator scheme
- A new finite difference discretization of order four for for two-dimensional quasi-linear elliptic boundary value problem
- Families of High Order Accurate Discretizations of Some Elliptic Problems
- Aspects of Numerical Methods for Elliptic Singular Perturbation Problems
- Fourth-order difference methods for the system of 2D nonlinear elliptic partial differential equations
- High accuracy finite difference approximation to solutions of elliptic partial differential equations
- On convergence and performance of iterative methods with fourth-order compact schemes
- Accuracy, robustness and efficiency comparison in iterative computation of convection diffusion equation with boundary layers
- High‐order compact scheme for the steady stream‐function vorticity equations
