456
Views
37
CrossRef citations to date
0
Altmetric
Original Article

A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters

, &
Pages 474-499 | Received 13 Jun 2016, Accepted 30 May 2017, Published online: 27 Mar 2018

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (7)

Genanew Gofe Gonfa & Imiru Takele Daba. (2024) Fitted numerical scheme for singularly perturbed parabolic differential- difference with time lag. Research in Mathematics 11:1.
Read now
Mrityunjoy B.S. Natesan & A. Sendur. (2023) Alternating direction implicit method for singularly perturbed 2D parabolic convection–diffusion–reaction problem with two small parameters. International Journal of Computer Mathematics 100:2, pages 253-282.
Read now
Imiru Takele Daba & Gemechis File Duressa. (2022) A novel algorithm for singularly perturbed parabolic differential-difference equations. Research in Mathematics 9:1.
Read now
Tesfaye Aga Bullo, Guy Aymard Degla & Gemechis File Duressa. (2022) Parameter-uniform finite difference method for singularly perturbed parabolic problem with two small parameters. International Journal for Computational Methods in Engineering Science and Mechanics 23:3, pages 210-218.
Read now
Sanjay Ku Sahoo & Vikas Gupta. (2021) Second-order parameter-uniform finite difference scheme for singularly perturbed parabolic problem with a boundary turning point. Journal of Difference Equations and Applications 27:2, pages 223-240.
Read now
Tariku Birabasa Mekonnen & Gemechis File Duressa. (2020) Computational method for singularly perturbed two-parameter parabolic convection-diffusion problems. Cogent Mathematics & Statistics 7:1.
Read now

Articles from other publishers (30)

Jasbir Singh, Naresh Kumar & Ram Jiwari. (2024) A robust weak Galerkin finite element method for two parameter singularly perturbed parabolic problems on nonuniform meshes. Journal of Computational Science 77, pages 102241.
Crossref
Gajendra Babu, M. Prithvi, Kapil K. Sharma & V. P. Ramesh. (2022) A Uniformly Convergent Numerical Algorithm on Harmonic ($$H(\ell )$$) Mesh for Parabolic Singularly Perturbed Convection-Diffusion Problems with Boundary Layer. Differential Equations and Dynamical Systems 32:2, pages 551-564.
Crossref
Khursheed J. Ansari, Mohammad Izadi & Samad Noeiaghdam. (2024) Enhancing the accuracy and efficiency of two uniformly convergent numerical solvers for singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters. Demonstratio Mathematica 57:1.
Crossref
Solomon Woldu Worku & Gemechis File Duressa. (2023) A Numerical Approach for Diffusion-Dominant Two-Parameter Singularly Perturbed Delay Parabolic Differential Equations. International Journal of Mathematics and Mathematical Sciences 2023, pages 1-17.
Crossref
Worku Tilahun Aniley & Gemechis File Duressa. (2023) Uniformly convergent numerical method for time-fractional convection–diffusion equation with variable coefficients. Partial Differential Equations in Applied Mathematics 8, pages 100592.
Crossref
Naol Tufa Negero. (2023) Fitted cubic spline in tension difference scheme for two-parameter singularly perturbed delay parabolic partial differential equations. Partial Differential Equations in Applied Mathematics 8, pages 100530.
Crossref
Sanjay Ku Sahoo & Vikas Gupta. (2023) Parameter robust higher‐order finite difference method for convection‐diffusion problem with time delay. Numerical Methods for Partial Differential Equations 39:6, pages 4145-4173.
Crossref
S. Priyadarshana & J. Mohapatra. (2023) An efficient computational technique for time dependent semilinear parabolic problems involving two small parameters. Journal of Applied Mathematics and Computing 69:5, pages 3721-3754.
Crossref
Tariku Birabasa Mekonnen & Gemechis File Duressa. (2023) Nonpolynomial Spline Method for Singularly Perturbed Time-Dependent Parabolic Problem with Two Small Parameters. Mathematical Problems in Engineering 2023, pages 1-15.
Crossref
Hakki Duru & Baransel Gunes. (2023) The stability and convergence analysis for singularly perturbed Sobolev problems with Robin type boundary condition. Georgian Mathematical Journal 30:3, pages 349-363.
Crossref
Mulunesh Amsalu Ayele, Awoke Andargie Tiruneh & Getachew Adamu Derese. (2023) Fitted cubic spline scheme for two-parameter singularly perturbed time-delay parabolic problems. Results in Applied Mathematics 18, pages 100361.
Crossref
Imiru Takele Daba & Gemechis File Duressa. (2023) Numerical treatment of singularly perturbed unsteady Burger-Huxley equation. Frontiers in Applied Mathematics and Statistics 8.
Crossref
Shan Jiang, Xiao Ding & Meiling Sun. (2023) PARAMETER-UNIFORM SUPERCONVERGENCE OF MULTISCALE COMPUTATION FOR SINGULAR PERTURBATION EXHIBITING TWIN BOUNDARY LAYERS. Journal of Applied Analysis & Computation 13:6, pages 3330-3351.
Crossref
S. Priyadarshana & J. Mohapatra. 2023. Proceedings of the Ninth International Conference on Mathematics and Computing. Proceedings of the Ninth International Conference on Mathematics and Computing 223 234 .
Satpal Singh, Parvin Kumari & Devendra Kumar. (2022) An effective numerical approach for two parameter time-delayed singularly perturbed problems. Computational and Applied Mathematics 41:8.
Crossref
Naol Tufa Negero. (2022) A uniformly convergent numerical scheme for two parameters singularly perturbed parabolic convection–diffusion problems with a large temporal lag. Results in Applied Mathematics 16, pages 100338.
Crossref
S. Priyadarshana, J. Mohapatra & S. R. Pattanaik. (2022) Parameter uniform optimal order numerical approximations for time-delayed parabolic convection diffusion problems involving two small parameters. Computational and Applied Mathematics 41:6.
Crossref
Dagnachew Mengstie Tefera, Awoke Andargie Tiruneh & Getachew Adamu Derese. (2022) Fitted Operator Method Using Multiple Fitting Factors for Two Parameters Singularly Perturbed Parabolic Problems. Mathematical Problems in Engineering 2022, pages 1-10.
Crossref
Subal Ranjan Sahu & Jugal Mohapatra. (2022) Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts. Journal of Applied Analysis 28:1, pages 121-134.
Crossref
Ram Jiwari, Sukhveer Singh & Paramjeet Singh. (2022) Local RBF-FD-Based Mesh-free Scheme for Singularly Perturbed Convection-Diffusion-Reaction Models with Variable Coefficients. Journal of Mathematics 2022, pages 1-11.
Crossref
Tesfaye Aga Bullo, Guy Aymard Degla & Gemechis File Duressa. (2022) Fitted mesh method for singularly perturbed parabolic problems with an interior layer. Mathematics and Computers in Simulation 193, pages 371-384.
Crossref
Tariku Birabasa Mekonnen & Gemechis File Duressa. (2022) A Fitted Mesh Cubic Spline in Tension Method for Singularly Perturbed Problems with Two Parameters. International Journal of Mathematics and Mathematical Sciences 2022, pages 1-11.
Crossref
Devendra Kumar & Komal Deswal. (2021) Wavelet-based approximation for two-parameter singularly perturbed problems with Robin boundary conditions. Journal of Applied Mathematics and Computing 68:1, pages 125-149.
Crossref
Subal Ranjan Sahu & Jugal Mohapatra. (2021) Numerical investigation of time delay parabolic differential equation involving two small parameters. Engineering Computations 38:6, pages 2882-2899.
Crossref
Tesfaye Aga Bullo, Gemechis File Duressa & Guy Aymard Degla. (2020) Robust Finite Difference Method for Singularly Perturbed Two-Parameter Parabolic Convection-Diffusion Problems. International Journal of Computational Methods 18:02, pages 2050034.
Crossref
Mukesh Kumar, Joginder Singh, Sunil Kumar & Aakansha Aakansha. (2020) A robust numerical method for a coupled system of singularly perturbed parabolic delay problems. Engineering Computations 38:2, pages 964-988.
Crossref
Meenakshi Shivhare, Pramod Chakravarthy Podila & Devendra Kumar. (2020) A uniformly convergent quadratic B-spline collocation method for singularly perturbed parabolic partial differential equations with two small parameters. Journal of Mathematical Chemistry 59:1, pages 186-215.
Crossref
Ritesh Kumar Dubey & Vikas Gupta. (2019) A Mesh Refinement Algorithm for Singularly Perturbed Boundary and Interior Layer Problems. International Journal of Computational Methods 17:07, pages 1950024.
Crossref
Sumit, Sunil Kumar, Kuldeep & Mukesh Kumar. (2020) A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem. Computational and Applied Mathematics 39:3.
Crossref
Akbar Barati Chiyaneh & Hakki Duru. (2019) On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems. Numerical Methods for Partial Differential Equations 36:2, pages 228-248.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.