High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems

DOI10.1016/j.apm.2012.02.020zbMath1349.65569OpenAlexW2067713762MaRDI QIDQ345760

Mohammad Hasan, M. Dambrine

Publication date: 2 December 2016

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2012.02.020

zbMATH Keywords

Burgers' equationdiffusion-convection equationReynolds numberquasi-linear elliptic equationcubic spline approximationPoisson's equation in polar coordinates

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Finite difference methods for boundary value problems involving PDEs (65N06)

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Cites Work

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• An \(O(h^4)\) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems
• Cubic spline solution of two-point boundary value problems with significant first derivatives
• 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
• Parametric cubic spline solution of two point boundary value problems
• Cubic spline solution of singularly perturbed boundary value problems with significant first derivatives
• A survey on parametric spline function approximation
• A new fourth order discretization for singularly perturbed two dimensional nonlinear elliptic boundary value problems
• A new finite difference discretization of order four for for two-dimensional quasi-linear elliptic boundary value problem
• High-accuracy cubic spline alternating group explicit methods for 1D quasi-linear parabolic equations†
• Convergence of $O(h^4 )$ Cubic Spline Collocation Methods for Elliptic Partial Differential Equations
• A fourth‐order difference method for elliptic equations with nonlinear first derivative terms
• On the use of splines for the numerical solution of nonlinear two-point boundary value problems
• Families of High Order Accurate Discretizations of Some Elliptic 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
• Spline methods for solving system of second-order boundary-value problems
• Iterative Line Cubic Spline Collocation Methods for Elliptic Partial Differential Equations in Several Dimensions
• A Fourth Order Accurate Cubic Spline Alternating Group Explicit Method For Non-Linear Singular Two Point Boundary Value Problems*
• Spline solution of non-linear singular boundary value problems
• Piecewise Cubic Interpolation and Two-Point Boundary Problems
• Cubic spline solutions to two-point boundary value problems
• The use of cubic splines in the solution of two-point boundary value problems
• Increased Accuracy Cubic Spline Solutions to Two-Point Boundary Value Problems
• The use of cubic splines in the numerical solution of a system of second-order boundary value problems

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