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S. Sumit, S. Kumar & M. Kumar. (2022) Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion problems. International Journal of Computer Mathematics 99:8, pages 1638-1653.
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Kuldeep & Sunil Kumar. (2022) An efficient finite difference method for coupled systems of singularly perturbed parabolic convection-diffusion problems. Journal of Difference Equations and Applications 28:5, pages 676-694.
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Pratibhamoy Das, Subrata Rana & Higinio Ramos. (2020) A perturbation-based approach for solving fractional-order Volterra–Fredholm integro differential equations and its convergence analysis. International Journal of Computer Mathematics 97:10, pages 1994-2014.
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S.N. Jator & N. Coleman. (2017) A nonlinear second derivative method with a variable step-size based on continued fractions for singular initial value problems. Cogent Mathematics 4:1.
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J.
E. Macías-Díaz & A. Puri. (2011) On some explicit non-standard methods to approximate nonnegative solutions of a weakly hyperbolic equation with logistic nonlinearity. International Journal of Computer Mathematics 88:15, pages 3308-3323.
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J. Ruiz-Ramírez & J.
E. Macías-Díaz. (2011) A finite-difference scheme to approximate non-negative and bounded solutions of a FitzHugh–Nagumo equation. International Journal of Computer Mathematics 88:15, pages 3186-3201.
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R. K. Mohanty & Divya Sharma. (2024) A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations. Journal of Mathematical Chemistry 62:5, pages 973-1011.
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B. Y. Datsko & M. V. Kutniv. (2024) Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs. Numerical Algorithms.
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Sumit Saini, Pratibhamoy Das & Sunil Kumar. (2024) Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time. Applied Numerical Mathematics 196, pages 1-21.
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K.C. Lee, M.A. Alias, N. Senu & A. Ahmadian. (2023)
On efficient frequency-dependent parameters of explicit two-derivative improved Runge-Kutta-Nystr
m method with application to two-body problem
. Alexandria Engineering Journal 72, pages 605-620.
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Sumit Saini, Pratibhamoy Das & Sunil Kumar. (2023) Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 117:2.
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Ram Shiromani, Vembu Shanthi & J. Vigo‐Aguiar. (2022) A finite difference method for a singularly perturbed 2‐D elliptic convection‐diffusion PDEs on Shishkin‐type meshes with non‐smooth convection and source terms. Mathematical Methods in the Applied Sciences 46:5, pages 5915-5936.
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Kinda Abuasbeh, Sania Qureshi, Amanullah Soomro & Muath Awadalla. (2023) An Optimal Family of Block Techniques to Solve Models of Infectious Diseases: Fixed and Adaptive Stepsize Strategies. Mathematics 11:5, pages 1135.
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Sania Qureshi, Amanullah Soomro, Evren Hincal, Jung Rye Lee, Choonkil Park & M.S. Osman. (2022) An efficient variable stepsize rational method for stiff, singular and singularly perturbed problems. Alexandria Engineering Journal 61:12, pages 10953-10963.
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Pramod Chakravarthy Podila, Vishwas Sundrani & Higinio Ramos. (2022) Numerical solution of a fourth‐order singularly perturbed boundary value problem with discontinuities via Haar wavelets. Mathematical Methods in the Applied Sciences 45:17, pages 10904-10916.
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Kuldeep & Sunil Kumar. (2022) Efficient High-Order Discretization Methods for Coupled Systems of Singularly Perturbed Parabolic Convection-Diffusion Problems. International Journal of Computational Methods 19:05.
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Sumit, Shashikant Kumar & Sunil Kumar. (2022) A high order convergent adaptive numerical method for singularly perturbed nonlinear systems. Computational and Applied Mathematics 41:2.
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Aakansha, Sunil Kumar & Joginder Singh. (2021) An efficient numerical method for coupled systems of singularly perturbed parabolic delay problems. Computational and Applied Mathematics 41:1.
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Saurabh Tomar, A. K. Verma & K. Vajravelu. (2021) An effective method for solving singular boundary value problems with some relevant physical applications. Computational and Applied Mathematics 41:1.
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Sania Qureshi, Amanullah Soomro & Evren Hınçal. (2022) A new family of 𝒜− acceptable nonlinear methods with fixed and variable stepsize approach. Computational and Mathematical Methods 3:6.
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Bohdan Datsko, Myroslaw Kutniv, Andriy Kunynets & Andrzej Włoch. (2020) New explicit high‐order one‐step methods for singular initial value problems. Computational and Mathematical Methods 3:3.
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Aakansha, Joginder Singh & Sunil Kumar. (2021) Additive schemes based domain decomposition algorithm for solving singularly perturbed parabolic reaction-diffusion systems. Computational and Applied Mathematics 40:3.
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L. Bayón, P. Fortuny Ayuso, V. M. García Fernández, C. Tasis, M. M. Ruiz & P. M. Suarez. (2020) Using the blow-up technique for a modified Lindemann mechanism. Journal of Mathematical Chemistry 59:1, pages 119-130.
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Sania Qureshi & Abdullahi Yusuf. (2020) A new third order convergent numerical solver for continuous dynamical systems. Journal of King Saud University - Science 32:2, pages 1409-1416.
Crossref
Crossref
M.V. Kutniv, B.Y. Datsko, A.V. Kunynets & A. Włoch. (2020) A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations. Applied Numerical Mathematics 148, pages 140-151.
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Pratibhamoy Das, Subrata Rana & Jesus Vigo-Aguiar. (2020) Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature. Applied Numerical Mathematics 148, pages 79-97.
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Pratibhamoy Das & Jesus Vigo-Aguiar. (2019) Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter. Journal of Computational and Applied Mathematics 354, pages 533-544.
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M. Chandru, P. Das & H. Ramos. (2018) Numerical treatment of two‐parameter singularly perturbed parabolic convection diffusion problems with non‐smooth data. Mathematical Methods in the Applied Sciences 41:14, pages 5359-5387.
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Pratibhamoy Das. (2015) Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems. Journal of Computational and Applied Mathematics 290, pages 16-25.
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Higinio Ramos & R. García-Rubio. (2009) Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009). Journal of Mathematical Chemistry 48:1, pages 98-108.
Crossref
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Higinio Ramos, J. Vigo-Aguiar, S. Natesan, R. García-Rubio & M. A. Queiruga. (2009) Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm. Journal of Mathematical Chemistry 48:1, pages 38-54.
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