Eurasian Journal of Science and Engineering
Volume 9 Issue 1 Article 7
Application of Lagrange Interpolation Method to Solve First-Order Differential Equation Using Newton Interpolation Approach
Author: Salisu Ibrahim1
1Mathematics Education Departments, Faculty of Education, Tishk International University-Erbil, Kurdistan Region, Iraq
Abstract: One of the important problems in mathematics is finding the analytic solution and numerical solution of the differential equation using various methods and techniques. Most of the researchers tackled different numerical approaches to solve ordinary differential equations. These methods such as the Runge Kutta method, Euler’s method, and Taylor’s polynomial method have so many issues like difficulties in finding the solution that can lead to singularities or no solution. In this work, we considered Newton’s interpolation and Lagrange’s interpolation polynomial method (LIPM). These studies combine both Newton’s interpolation method and Lagrange method (NIPM) to solve first-order differential equations. The results obtained provide minimum approximative error. The result is supported by solving an example.
Keywords: Differential Equation, Lagrange Interpolation Method, Newton Interpolation First-order Differential Equation
Published: January 12, 2023
References
Faith, C. (2018). Solution of first order differential equation using numerical newton’s interpolation and lagrange method. Int. J. Dev. Res, 8, 18973-18976.
Faith, C. K., & Seeam, A. K. (2018). Knowledge sharing in academia: A case study using a SECI model approach. J. Educ, 9, 53-70.
Cuneyt, I. E., S Cansun, D., Ibrahim F, U., F Tuncay, O., & Oktay, K. (2004). Comparison of lipid profiles in normal and hypertensive pregnant women.
Ibrahim, S. (2020). Numerical Approximation Method for Solving Differential Equations. Eurasian Journal of Science & Engineering, 6(2), 157-168, 2020.
Ibrahim, S., & Isah, A. (2021). Solving System of Fractional Order Differential Equations Using Legendre Operational Matrix of Derivatives. Eurasian Journal of Science & Engineering, 7(1), 25-37, 2021.
Ibrahim, S., & Isah, A. (2022). Solving Solution for Second-Order Differential Equation Using Least Square Method. Eurasian Journal of Science & Engineering, 8(1), 119-125, 2022.
Ibrahim, S., & Koksal, M. E. (2021a). Commutativity of Sixth-Order Time-Varying Linear Systems. Circuits Syst Signal Process, 2021a. https://doi.org/10.1007/s00034-021-01709-6
Ibrahim, S., & Koksal, M. E. (2021b). Realization of a Fourth-Order Linear Time-Varying Differential System with Nonzero Initial Conditions by Cascaded two Second-Order Commutative Pairs. Circuits Syst Signal Process, 2021b. https://doi.org/10.1007/s00034-020-01617-1.
Isah, A., & Ibrahim, S. (2021). Shifted Genocchi Polynomial Operational Matrix for Solving Fractional Order System. Eurasian Journal of Science & Engineering, 7(1) 25-37, 2021.
Islam, S., Khan, Y., Faraz, N., & Austin, F. (2010). Numerical solution of logistic differential equations by using the Laplace decomposition method.
Ide, N.-A.-D. (2008). A new Hybrid iteration method for solving algebraic equations. Applied Mathematics and Computation, 195(2), 772-774.
Islam, M. E., & Akbar, M. A. (2020). Stable wave solutions to the Landau-Ginzburg-Higgs equation and the modified equal width wave equation using the IBSEF method. Arab Journal of Basic and Applied Sciences, 27(1), 270-278.
Kreuzberger, N., Damen, J. A., Trivella, M., Estcourt, L. J., Aldin, A., Umlauff, L., . . . Monsef, I. (2020). Prognostic models for newly‐diagnosed chronic lymphocytic leukaemia in adults: a systematic review and meta‐analysis. Cochrane Database of Systematic Reviews(7).
Rababah, A., & Ibrahim, S. (2016a). Weighted G^1-Multi-Degree Reduction of Bézier Curves. International Journal of Advanced Computer Science and Applications, 7(2), 540-545, 2016a. https://thesai.org/Publications/ViewPaper?Volume=7&Issue=2&Code=ijacsa&SerialNo=70
Rababah, A., & Ibrahim, S. (2016b). Weighted Degree Reduction of Bézier Curves with G^2-continuity. International Journal of Advanced and Applied Science, 3(3), 13-18, 2016b.
Rababah, A., & Ibrahim, S. (2018). Geometric Degree Reduction of Bézier curves, Springer Proceeding in Mathematics and Statistics, Book Chapter 8. 2018. https://springer.com/us/book/9789811320941
Salisu, I. (2022a). Commutativity of high-order linear time-varying systems. Advances in Differential Equations and Control Processes 27(1) (2022a), 73-83. https://dx.doi.org/10.17654/0974324322013
Salisu, I.(2022b). Discrete least square method for solving differential equations, Advances and Applications in Discrete Mathematics 30 (2022b), 87-102. https://dx.doi.org/10.17654/0974165822021
Salisu, I.(2022c). Commutativity associated with Euler second-order Differential Equation. Advances in Differential Equations and Control Processes 28(1) (2022c), 29-36. https://dx.doi.org/10.17654/0974324322013
Salisu, I., & Abedallah R. (2022). Decomposition of Fourth-Order Euler-Type Linear Time-Varying Differential System into Cascaded Two Second-Order Euler Commutative Pairs, Complexity, 2022. https://doi.org/10.1155/2022/3690019.
Sauer, T. (2004). Lagrange interpolation on subgrids of tensor product grids. Mathematics of Computation, 73(245), 181-190.
Weber, G. (1975). Energetics of ligand binding to proteins Advances in protein chemistry (Vol. 29, pp. 1-83): Elsevier.
Zhao, L., Wang, J., Li, Y., Song, T., Wu, Y., Fang, S., . . . Pei, D. (2021). NONCODEV6: an updated database dedicated to long non-coding RNA annotation in both animals and plants. Nucleic acids research, 49(D1), D165-D171.
Zill, D. G. (2012). A first course in differential equations with modeling applications: Cengage Learning.
Zou, L., Song, L., Wang, X., Weise, T., Chen, Y., & Zhang, C. (2020). A new approach to Newton-type polynomial interpolation with parameters. Mathematical Problems in Engineering, 2020.