Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 7, pp. 2387 - 2403

In this article, we propose a second-order uniformly convergent numerical method for a singularly perturbed 2D parabolic convectionâ€“diffusion...

Finite difference scheme | Uniform convergence | Richardson extrapolation technique | Piecewise-uniform Shishkin meshes | Fractional-step method | Singularly perturbed 2D parabolic convectionâ€“diffusion problems | SCHEME | MATHEMATICS, APPLIED | RICHARDSON EXTRAPOLATION | Singularly perturbed 2D parabolic convection-diffusion problems

Finite difference scheme | Uniform convergence | Richardson extrapolation technique | Piecewise-uniform Shishkin meshes | Fractional-step method | Singularly perturbed 2D parabolic convectionâ€“diffusion problems | SCHEME | MATHEMATICS, APPLIED | RICHARDSON EXTRAPOLATION | Singularly perturbed 2D parabolic convection-diffusion problems

Journal Article

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2019, Volume 59, Issue 1, pp. 207 - 225

In this article, we study the numerical solution of a singularly perturbed 2D delay parabolic convectionâ€“diffusion problem. First, we discretize the domain...

Uniform convergence | Piecewise-uniform Shishkin mesh | Computational Mathematics and Numerical Analysis | Singularly perturbed 2D delay parabolic problems | Mathematics of Computing | 65M06 | Mathematical and Computational Engineering | Mathematics | Theory of Computation | 65M12 | Boundary layers | Upwind scheme | MATHEMATICS | SCHEME | MATHEMATICS, APPLIED | Derivatives (Financial instruments) | Analysis | Methods | Boundary layer | Parameter estimation | Stability analysis | Parameters | Numerical analysis | Convection | Delay

Uniform convergence | Piecewise-uniform Shishkin mesh | Computational Mathematics and Numerical Analysis | Singularly perturbed 2D delay parabolic problems | Mathematics of Computing | 65M06 | Mathematical and Computational Engineering | Mathematics | Theory of Computation | 65M12 | Boundary layers | Upwind scheme | MATHEMATICS | SCHEME | MATHEMATICS, APPLIED | Derivatives (Financial instruments) | Analysis | Methods | Boundary layer | Parameter estimation | Stability analysis | Parameters | Numerical analysis | Convection | Delay

Journal Article

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 6/2019, Volume 60, Issue 1, pp. 51 - 86

This article focuses on developing and analyzing an efficient numerical scheme for solving two-dimensional singularly perturbed parabolic convectionâ€“diffusion...

Bakhvalovâ€“Shishkin mesh uniform convergence | Computational Mathematics and Numerical Analysis | 65M06 | Mathematics | Theory of Computation | Regular boundary layer | Piecewise-uniform Shishkin mesh | Numerical scheme | Mathematics of Computing | Mathematical and Computational Engineering | CR G1.8 | Alternating directions | Singularly perturbed parabolic problem | 65M12 | MATHEMATICS | Bakhvalov-Shishkin mesh uniform convergence | MATHEMATICS, APPLIED | Time dependence | Diffusion layers | Alternating direction implicit methods | Boundary value problems | Parameters | Convection | Boundary layers | Convergence | Finite difference method

Bakhvalovâ€“Shishkin mesh uniform convergence | Computational Mathematics and Numerical Analysis | 65M06 | Mathematics | Theory of Computation | Regular boundary layer | Piecewise-uniform Shishkin mesh | Numerical scheme | Mathematics of Computing | Mathematical and Computational Engineering | CR G1.8 | Alternating directions | Singularly perturbed parabolic problem | 65M12 | MATHEMATICS | Bakhvalov-Shishkin mesh uniform convergence | MATHEMATICS, APPLIED | Time dependence | Diffusion layers | Alternating direction implicit methods | Boundary value problems | Parameters | Convection | Boundary layers | Convergence | Finite difference method

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2017, Volume 313, pp. 453 - 473

In this article, we study the numerical solution of singularly perturbed 2D degenerate parabolic convection-diffusion problems on a rectangular domain. The...

Singularly perturbed 2D degenerate parabolic convection-diffusion problem | Finite difference scheme | Uniform convergence | Alternating direction scheme | Piecewise-uniform Shishkin meshes | TWIN BOUNDARY-LAYERS | MATHEMATICS, APPLIED | parabolic convection-diffusion problem | Singularly perturbed 2D degenerate | ALGORITHM | MESH | EQUATION | Boundary layer

Singularly perturbed 2D degenerate parabolic convection-diffusion problem | Finite difference scheme | Uniform convergence | Alternating direction scheme | Piecewise-uniform Shishkin meshes | TWIN BOUNDARY-LAYERS | MATHEMATICS, APPLIED | parabolic convection-diffusion problem | Singularly perturbed 2D degenerate | ALGORITHM | MESH | EQUATION | Boundary layer

Journal Article

Numerical Algorithms, ISSN 1017-1398, 07/2017, Volume 75, Issue 3, pp. 809 - 826

In this work, we are concerned with the efficient resolution of two dimensional parabolic singularly perturbed problems of convection-diffusion type. The...

Uniform convergence | Convection-diffusion | Piecewise uniform meshes | Singularly perturbed problems | Order reduction | Fractional euler method | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Methods | Algorithms

Uniform convergence | Convection-diffusion | Piecewise uniform meshes | Singularly perturbed problems | Order reduction | Fractional euler method | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Methods | Algorithms

Journal Article

International Journal of Applied and Computational Mathematics, ISSN 2349-5103, 4/2018, Volume 4, Issue 2, pp. 1 - 23

In this article, we are interested to approximate the solution of a singularly perturbed 2D delay parabolic convectionâ€“diffusion initial-boundary-value...

Uniform convergence | 65M15 | Theoretical, Mathematical and Computational Physics | 65M06 | Singularly perturbed 2D delay parabolic convectionâ€“diffusion problems | Fractional step method | Mathematics | Computational Science and Engineering | Finite difference scheme | Piecewise-uniform Shishkin meshes | Operations Research/Decision Theory | Nuclear Energy | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | 65M12 | Boundary layers

Uniform convergence | 65M15 | Theoretical, Mathematical and Computational Physics | 65M06 | Singularly perturbed 2D delay parabolic convectionâ€“diffusion problems | Fractional step method | Mathematics | Computational Science and Engineering | Finite difference scheme | Piecewise-uniform Shishkin meshes | Operations Research/Decision Theory | Nuclear Energy | Applications of Mathematics | Mathematical Modeling and Industrial Mathematics | 65M12 | Boundary layers

Journal Article

International Journal of Mathematical Modelling and Numerical Optimisation, ISSN 2040-3607, 2018, Volume 8, Issue 4, pp. 305 - 330

In this paper, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve this problem...

Finite difference scheme | Uniform convergence | Singularly perturbed 2D delay parabolic convection-diffusion problems | Bakhvalov-Shishkin mesh | Boundary layers | Boundary value problems | Discretization | Numerical methods | Delay | Mesh generation | Convergence | Convection-diffusion equation | Finite difference method

Finite difference scheme | Uniform convergence | Singularly perturbed 2D delay parabolic convection-diffusion problems | Bakhvalov-Shishkin mesh | Boundary layers | Boundary value problems | Discretization | Numerical methods | Delay | Mesh generation | Convergence | Convection-diffusion equation | Finite difference method

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 10/2017, Volume 43, Issue 5, pp. 885 - 909

A linear singularly perturbed elliptic problem, of convection-diffusion type, posed on a circular domain is examined. Regularity constraints are imposed on the...

Visualization | 65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Circular domain | Mathematical and Computational Biology | 65N06 | Convection-diffusion | Mathematics | Computational Science and Engineering | Singularly perturbed | Shishkin mesh | Mathematical Modeling and Industrial Mathematics | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | EQUATIONS | BOUNDARY-LAYER THEORY | CIRCLE | Usage | Mathematical models | Research | Singularities (Mathematics) | Mathematical research | Perturbation (Mathematics)

Visualization | 65N15 | Computational Mathematics and Numerical Analysis | 65N12 | Circular domain | Mathematical and Computational Biology | 65N06 | Convection-diffusion | Mathematics | Computational Science and Engineering | Singularly perturbed | Shishkin mesh | Mathematical Modeling and Industrial Mathematics | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | EQUATIONS | BOUNDARY-LAYER THEORY | CIRCLE | Usage | Mathematical models | Research | Singularities (Mathematics) | Mathematical research | Perturbation (Mathematics)

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 01/2006, Volume 46, Issue 1, pp. 49 - 72

A boundary value problem for a singularly perturbed parabolic convection-diffusion equation on an interval is considered. The higher order derivative in the...

Singularly perturbed boundary value problem | Finite difference approximation | Piecewise smooth initial condition | Special grids | Additive separation of singularities | Parabolic convection-diffusion equation | Convergence | Intervals | Boundary value problems | Approximation | Mathematical analysis | Mathematical models | Derivatives | Boundary layer | Convection-diffusion equation

Singularly perturbed boundary value problem | Finite difference approximation | Piecewise smooth initial condition | Special grids | Additive separation of singularities | Parabolic convection-diffusion equation | Convergence | Intervals | Boundary value problems | Approximation | Mathematical analysis | Mathematical models | Derivatives | Boundary layer | Convection-diffusion equation

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 2/2006, Volume 46, Issue 2, pp. 231 - 250

The Dirichlet problem on an interval for quasilinear singularly perturbed parabolic convection-diffusion equation is considered. The higher order derivative of...

Computational Mathematics and Numerical Analysis | domain decomposition | singularly perturbed Dirichlet problem | improved accuracy | Mathematics | quasilinear parabolic convection-diffusion equation | method of asymptotic constructions | piecewise uniform grids | Singularly perturbed Dirichlet problem | Piecewise uniform grids | Method of asymptotic constructions | Improved accuracy | Domain decomposition | Quasilinear parabolic convection-diffusion equation | Studies | Intervals | Construction | Approximation | Asymptotic properties | Mathematical analysis | Mathematical models | Derivatives | Boundary layer

Computational Mathematics and Numerical Analysis | domain decomposition | singularly perturbed Dirichlet problem | improved accuracy | Mathematics | quasilinear parabolic convection-diffusion equation | method of asymptotic constructions | piecewise uniform grids | Singularly perturbed Dirichlet problem | Piecewise uniform grids | Method of asymptotic constructions | Improved accuracy | Domain decomposition | Quasilinear parabolic convection-diffusion equation | Studies | Intervals | Construction | Approximation | Asymptotic properties | Mathematical analysis | Mathematical models | Derivatives | Boundary layer

Journal Article

Computing, ISSN 0010-485X, 12/1998, Volume 61, Issue 4, pp. 331 - 357

A finite difference method is presented for singularly perturbed convection-diffusion problems with discretization error estimate of nearly second order. In a...

65N15 | Singularly perturbed convection-diffusion problems | Computational Mathematics and Numerical Analysis | interpolation | skew stencil | 35B25 | adaptive refinement | 65N06 | 65N50 | Mathematics | finite differences | defect-correction technique | Adaptive refinement | Interpolation | Skew stencil | Finite differences | Defect-correction technique | COMPUTER SCIENCE, THEORY & METHODS | singularly perturbed convection-diffusion problems

65N15 | Singularly perturbed convection-diffusion problems | Computational Mathematics and Numerical Analysis | interpolation | skew stencil | 35B25 | adaptive refinement | 65N06 | 65N50 | Mathematics | finite differences | defect-correction technique | Adaptive refinement | Interpolation | Skew stencil | Finite differences | Defect-correction technique | COMPUTER SCIENCE, THEORY & METHODS | singularly perturbed convection-diffusion problems

Journal Article

Computing, ISSN 0010-485X, 1997, Volume 58, Issue 1, pp. 1 - 30

A difference method is presented for singularly perturbed convection-diffusion problems with discretization error estimates of high order (orderp), which hold...

65N15 | Computational Mathematics and Numerical Analysis | 35B25 | Singularly perturbed convection-diffusion problem | 65N06 | 65N50 | adaptive refinement strategies | Mathematics | finite differences | order of discretization error | defect-correction technique | Adaptive refinement strategies | Finite differences | Defect-correction technique | Order of discretization error | singularly perturbed convection-diffusion problem | LOCAL REFINEMENT | ELEMENT METHODS | COMPUTER SCIENCE, THEORY & METHODS | K EX COMPUTER SCIENCE, THEORY & METHODS

65N15 | Computational Mathematics and Numerical Analysis | 35B25 | Singularly perturbed convection-diffusion problem | 65N06 | 65N50 | adaptive refinement strategies | Mathematics | finite differences | order of discretization error | defect-correction technique | Adaptive refinement strategies | Finite differences | Defect-correction technique | Order of discretization error | singularly perturbed convection-diffusion problem | LOCAL REFINEMENT | ELEMENT METHODS | COMPUTER SCIENCE, THEORY & METHODS | K EX COMPUTER SCIENCE, THEORY & METHODS

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2002, Volume 39, Issue 2, pp. 690 - 707

Using the theory of n-widths, the approximability in L2 of solutions of a singularly perturbed linear convection-diffusion problem in two dimensions is...

Integers | Unit ball | Boundary value problems | Approximation | Differential equations | Boundary conditions | Mathematical constants | Mathematical functions | Boundary layers | Triangle inequalities | Convection-diffusion | n-width | Singularly perturbed | Differential equation | MATHEMATICS, APPLIED | singularly perturbed | differential equation | convection-diffusion

Integers | Unit ball | Boundary value problems | Approximation | Differential equations | Boundary conditions | Mathematical constants | Mathematical functions | Boundary layers | Triangle inequalities | Convection-diffusion | n-width | Singularly perturbed | Differential equation | MATHEMATICS, APPLIED | singularly perturbed | differential equation | convection-diffusion

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 08/2009, Volume 49, Issue 8, pp. 1348 - 1368

The Dirichlet problem for a singularly perturbed parabolic reaction-diffusion equation with a piecewise continuous initial condition in a rectangular domain is...

Piecewise continuous initial condition | Singularly perturbed boundary value problem | Special grids | Method of additive splitting of singularities | Îµ-uniform convergence | Richardson technique | Parabolic reaction-diffusion equation | Grid approximation | special grids | MATHEMATICS, APPLIED | grid approximation | APPROXIMATION | piecewise continuous initial condition | PHYSICS, MATHEMATICAL | parabolic reaction-diffusion equation | singularly perturbed boundary value problem | method of additive splitting of singularities | epsilon-uniform convergence | Boundary layer | Studies | Mathematical analysis

Piecewise continuous initial condition | Singularly perturbed boundary value problem | Special grids | Method of additive splitting of singularities | Îµ-uniform convergence | Richardson technique | Parabolic reaction-diffusion equation | Grid approximation | special grids | MATHEMATICS, APPLIED | grid approximation | APPROXIMATION | piecewise continuous initial condition | PHYSICS, MATHEMATICAL | parabolic reaction-diffusion equation | singularly perturbed boundary value problem | method of additive splitting of singularities | epsilon-uniform convergence | Boundary layer | Studies | Mathematical analysis

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 06/2012, Volume 33, Issue 6, pp. 638 - 660

The motive of the current study is to derive pointwise error estimates for the three-step Taylor Galerkin finite element method for singularly perturbed...

Finite element method | Uniform convergence | Taylor Galerkin method | Error estimates | Secondary 35K55 | Exponentially fitted splines | Singularly perturbed | Mass-lumped | Boundary layer | Primary 74S05, 65M06 | MATHEMATICS, APPLIED | BOUNDARY-LAYER | TURNING-POINTS | DIFFERENCE-SCHEMES

Finite element method | Uniform convergence | Taylor Galerkin method | Error estimates | Secondary 35K55 | Exponentially fitted splines | Singularly perturbed | Mass-lumped | Boundary layer | Primary 74S05, 65M06 | MATHEMATICS, APPLIED | BOUNDARY-LAYER | TURNING-POINTS | DIFFERENCE-SCHEMES

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 3/2007, Volume 47, Issue 3, pp. 442 - 462

A problem for the black-Scholes equation that arises in financial mathematics is reduced, by a transformation of variables, to the Cauchy problem for a...

additive splitting of singularities | Computational Mathematics and Numerical Analysis | nonsmooth initial data | convergence | interior layer | Black-Scholes equation | Mathematics | singularly perturbed parabolic equation | difference scheme | Difference scheme | Nonsmooth initial data | Additive splitting of singularities | Singularly perturbed parabolic equation | Convergence | Interior layer | Studies | Discontinuity | Construction | Approximation | Singularities | Mathematical analysis | Mathematical models | Derivatives

additive splitting of singularities | Computational Mathematics and Numerical Analysis | nonsmooth initial data | convergence | interior layer | Black-Scholes equation | Mathematics | singularly perturbed parabolic equation | difference scheme | Difference scheme | Nonsmooth initial data | Additive splitting of singularities | Singularly perturbed parabolic equation | Convergence | Interior layer | Studies | Discontinuity | Construction | Approximation | Singularities | Mathematical analysis | Mathematical models | Derivatives

Journal Article

Numerical Algorithms, ISSN 1017-1398, 10/2000, Volume 24, Issue 4, pp. 333 - 355

Numerical methods for the incompressible Reynolds-averaged Navier-Stokes equations discretized by finite difference techniques on collocated cell-centered...

incompressible Navier-Stokes equations | Numeric Computing | Krylov subspace method | robustness | Theory of Computation | 76D05 | 76M20 | Algebra | Algorithms | 65F10 | Computer Science | Mathematics, general | 65N55 | multigrid method | semicoarsening | Multigrid method | Robustness | Incompressible Navier-Stokes equations | Semicoarsening | INTERFACE PROBLEMS | MATHEMATICS, APPLIED | GRIDS | SINGULARLY PERTURBED PROBLEMS | NONSYMMETRIC LINEAR-SYSTEMS

incompressible Navier-Stokes equations | Numeric Computing | Krylov subspace method | robustness | Theory of Computation | 76D05 | 76M20 | Algebra | Algorithms | 65F10 | Computer Science | Mathematics, general | 65N55 | multigrid method | semicoarsening | Multigrid method | Robustness | Incompressible Navier-Stokes equations | Semicoarsening | INTERFACE PROBLEMS | MATHEMATICS, APPLIED | GRIDS | SINGULARLY PERTURBED PROBLEMS | NONSYMMETRIC LINEAR-SYSTEMS

Journal Article

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