Volume 4 • Issue 2 • PP: 43-47 • 2024
Accurate Numerical Method Using Exponential Spline for solving boundary Value Problems
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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This study introduces a precise numerical technique employing exponential splines for singly perturbed singularity boundary values problems. A numerical scheme is devised to address issues encountered in diverse scientific and engineering domains. The framework consists of a triad of nonlinear equations. The approach is employed in several test cases to demonstrate accuracy and implementation.
Keywords
References
[1] Bawa RK. Spline based computational technique for linear singularly perturbed boundary value problems. Appl Math Comput 2005;167:225–36. https://doi.org/10.1016/j.amc.2004.06.112.
[2] Chandru M, Prabha T, Das P, Shanthi V. A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problems with Discontinuous Convection Coefficient and Source Terms. Differ Equations Dyn Syst 2017;27:91–112. https://doi.org/10.1007/s12591-017-0385-3.
[3] Mohapatra J, Shakti D. Numerical treatment for the solution of singularly perturbed pseudo-parabolic problem on an equidistributed grid. Nonlinear Eng 2020;9:169–74. https://doi.org/10.1515/nleng-2020-0006.
[4] Nikolis A, Seimenis I. Solving dynamical systems with cubic trigonometric splines. Appl Math E-Notes [Electronic Only] 2005;5:116–23.
[5] Vijayakumar V, Udhayakumar R, Kavitha K. On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay. Evol Equations & Control Theory 2021;10:271–396. https://doi.org/10.3934/eect.2020066.
[6] Zahra WK. Trigonometric B-Spline Collocation Method for Solving PHI-Four and Allen–Cahn Equations. Mediterr J Math 2017;14. https://doi.org/10.1007/s00009-017-0916-8.
[7] Chandru M, Shanthi V. Fitted Mesh Method for Singularly Perturbed Robin Type Boundary Value Problem with Discontinuous Source Term. Int J Appl Comput Math 2015;1:491–501. https://doi.org/10.1007/s40819-015-0030-1.
[8] Chandru M, Shanthi V. An asymptotic numerical method for singularly perturbed fourth order ODE of convection-diffusion type turning point problem. Neural, Parallel, Sci Comput 2016;24:473–88.
[9] Debela HG, Duressa GF. Uniformly convergent numerical method for singularly perturbed <scp>convection‐diffusion</scp> type problems with nonlocal boundary condition. Int J Numer Methods Fluids 2020;92:1914–26. https://doi.org/10.1002/fld.4854.
[10] Debela HG, Duressa GF. Accelerated Exponentially Fitted Operator Method for Singularly Perturbed Problems with Integral Boundary Condition. Int J Differ Equations 2020;2020:1–8. https://doi.org/10.1155/2020/9268181.
[11] Debela HG, Duressa GF. Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition. J Egypt Math Soc 2020;28:1–16.
[12] Jiwari R, Singh S, Singh P. Local RBF‐FD‐Based Mesh‐free Scheme for Singularly Perturbed Convection‐Diffusion‐Reaction Models with Variable Coefficients. J Math 2022;2022. https://doi.org/10.1155/2022/3119482.
[13] Kadalbajoo MK, Patidar KC. Singularly perturbed problems in partial differential equations: a survey. Appl Math Comput 2003;134:371–429. https://doi.org/10.1016/s0096-3003(01)00291-0.
[14] Kumar N, Toprakseven Ş, Jiwari R. A numerical method for singularly perturbed convection–diffusion–reaction equations on polygonal meshes. Comput Appl Math 2024;43. https://doi.org/10.1007/s40314-023-02553-x.
[15] Hepson OE, Dag I. Numerical Solution of Singularly Perturbed Problems via both Galerkin and Subdomain Galerkin methods. Appl Math & Inf Sci 2018;12:495–500. https://doi.org/10.18576/amis/120303.
[16] Khan MA, Tirmizi IA, Twizell EH. Non polynomial spline approach to the solution of a system of third-order boundary-value problems. Appl Math Comput 2005;168:152–63.
[17] Rashidinia J, Mohammadi R. Non-Polynomial Spline approximations for the solution of singularlyperturbed boundary value problems. TWMS J Pure Appl Math 2010;1:236–51.
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