A collection of computational techniques for solving singular boundary-value problems

DOI10.1016/j.advengsoft.2008.04.010zbMath1159.65076OpenAlexW2031849203MaRDI QIDQ1005573

Neelima Singh, Manoj Kumar

Publication date: 9 March 2009

Published in: Advances in Engineering Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.advengsoft.2008.04.010

zbMATH Keywords

singular perturbationfinite difference methodB-splineGalerkin spectral methodChebychev economizationtwo-point singular boundary-value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for ordinary differential equations (34B15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items

A rational spectral collocation method for third-order singularly perturbed problems, Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution, Solving singular two-point boundary value problems using continuous genetic algorithm, Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey, Rational spectral collocation combined with singularity separation method for second-order singular perturbation problems, Direct expansion method of boundary condition for solving 3D elliptic equations with small parameters in the irregular domain, Unnamed Item, Asymptotic and numerical methods in estimating eigenvalues, Computer simulation of third‐order nonlinear singular problems arising in draining and coating flows, Numerical solution of singular regular boundary value problems by pole detection with qd-algorithm, Numerical solutions for the linear and nonlinear singular boundary value problems using Laguerre wavelets, Rational spectral collocation combined with the singularity separated method for a system of singularly perturbed boundary value problems, Numerical Solution of Singularly Perturbed Two-point BVPs Using Nonuniform Haar Wavelets, Solving a class of singular two-point boundary value problems using new effective reproducing kernel technique, Novel functional matrix method using standard basis of polynomial linear space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A family of variable mesh methods for the estimates of (d\(u\)/d\(r\)) and solution of non-linear two point boundary value problems with singularity
• The singular finite element method for some elliptic boundary value problem with interface
• Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations
• An \(O(h^4)\) accurate cubic spline TAGE method for nonlinear singular two point boundary value problems
• Existence and uniqueness of positive solution for singular boundary value problem
• A TAGE iterative method for the solution of nonlinear singular two point boundary value problems using a sixth order discretization
• A uniform mesh finite difference method for a class of singular two-point boundary value problems
• Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms
• Nontrivial solutions of singular sublinear Sturm--Liouville problems
• Numerical study for a class of singular two-point boundary value problems using Green's functions
• Diffusion problems with a mixed nonlinear boundary condition
• Sextic spline solution of a singularly perturbed boundary-value problem
• Variable mesh methods for the numerical solution of two-point singular perturbation problems
• Order \(h^ 2\) method for a singular two-point boundary value problem
• On the existence of solutions of a class of singular nonlinear two-point boundary value problems
• Spline finite difference methods for singular two point boundary value problems
• Finite difference methods and their convergence for a class of singular two point boundary value problems
• Singular two point boundary value problems for second order differential equations
• On a collocation method for singular two point boundary value problems
• Singular two point boundary value problems for second order differential systems
• A reliable modification of Adomian decomposition method
• Positive solutions for a class of nonlinear singular boundary value problems at resonance
• On a class of regular singular two point boundary value problems
• Order \(h^ 4\) difference methods for a class of singular two space elliptic boundary value problems
• A collocation method for solving a class of singular nonlinear two-point boundary value problems
• A difference method for singular two-point boundary value problems
• An iterative shooting method for a certain class of singular two-point boundary value problems.
• On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology.
• Quintic spline approach to the solution of a singularly-perturbed boundary-value problem
• A three-point finite difference method for a class of singular two-point boundary value problems
• Numerical solution of singular boundary value problems via Chebyshev polynomial and B-spline
• Projection methods and singular two point boundary value problems
• Integral methods for computing solutions of a class of singular two-point boundary value problems
• Method of reduction of order for solving singularly perturbed two-point boundary value problems
• A spline method for second-order singularly perturbed boundary-value problems
• Cubic spline for solving singular two-point boundary value problems
• Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh
• A family of nonuniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives
• On the convergence of finite difference methods for weakly regular singular boundary value problems
• Cubic spline for a class of nonlinear singular boundary value problems arising in physiology
• An efficient numerical method for singular perturbation problems
• A new fourth order discretization for singularly perturbed two dimensional nonlinear elliptic boundary value problems
• A sinc-collocation method with boundary treatment for two-dimensional elliptic boundary value problems
• Sinc collocation method with boundary treatment for two-point boundary value problems
• On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems
• Numerical methods of high-order accuracy for singular nonlinear boundary value problems
• A numerical method for solving singular boundary value problems
• Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines
• Solving two point boundary value problems by interpolatory subdivision algorithms
• Numerical Methods for Singular Boundary Value Problems
• Convergence of Adomian's Method
• Group explicit iterative methods for solving large linear systems
• A Uniform Mesh Finite Difference Method for a Class of Singular Two-Point Boundary Value Problems
• High-order methods for elliptic equations with variable coefficients
• A New Fourth Order Cubic Spline Method for Non-Linear Two-Point Boundary Value Problems
• Singular sturm liouville problems and existence of solutions to singular nonlinear boundary value problems
• Fourth order finite difference methods for the system of 2-d nonlinear elliptic equations with variable coefficients
• An iterative scheme for solving nonlinear two point boundary value problems
• Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
• The Modified Adomian Decomposition Method for Solving Linear and Nonlinear Boundary Value Problems of Tenth-order and Twelfth-order
• A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems
• On a class of weakly regular singular two point boundary value problems—I
• Iterative methods for solving non-linear two point boundary value problems
• A different approach for solving singular two‐point boundary value problems
• Correction method and extrapolation method for singular two-point boundary value problems
• Defect correction on Shishkin-type meshes
• Tikhonov regularization of an elliptic PDE
• Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems
• Discrete boundary conditions for problems with interface
• Approximation of derivatives in a convection-diffusion two-point boundary value problem
• A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems