Solving coupled non-linear higher order BVPs using improved shooting method
By:
References
- Azarnavid B., Emamjomeh M., Nabati M., A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem, Chaos Solitons and Fractals, 159, 112159, 2022.
- Miele A., Well K.H., Tietze J.L., Multipoint approach to the two-point boundary value problem, Journal of Mathematical Analysis and Applications, 44(3), 625–642, 1973.
- Uçar Y., Yağmurlu N.M., Yiğgit M.K., Numerical solution of the coupled Burgers equation by trigonometric B-spline collocation method, Mathematical Methods in the Applied Sciences, 46(5), 6025–6041, 2023.
- Yağmurlu N.M., Gagir A., A finite difference approximation for numerical simulation of 2D viscous coupled Burgers equations, Mathematical Sciences and Applications E-Notes, 10(3), 146–158, 2022.
- Yağmurlu N.M., Gagir A., Numerical simulation of two dimensional coupled Burgers equations by Rubin-Graves type linearization, Mathematical Sciences and Applications E-Notes, 9(4), 158–169, 2021.
- Morrison D., Riley J.D., Zancanaro J.F., Multiple shooting method for two-point boundary value problems, Communications of the ACM, 5(12), 613–614, 1962.
- Keller H.B., Numerical Solution of Two Point Boundary Value Problems, Society for Industrial and Applied Mathematics, Philadelphia, USA, 1976.
- Matinfar M., Ghasemi M., Solving BVPs with shooting method and VIMHP, Journal of the Egyptian Mathematical Society, 21(3), 354–360, 2013.
- Singh J., A nonlinear shooting method and its application to nonlinear Rayleigh-Bénard convection, International Scholarly Research Notices, 2013(650208), 1–9, 2013.
- Javeed S., Shabnam A., Baleanu D., An improved shooting technique for solving boundary value problems using higher order initial approximation algorithms, Punjab University Journal of Mathematics, 51(11), 101–113, 2019.
- Jones D.J., Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems, Journal of Computational and Applied Mathematics, 47(3), 395–400, 1993.
- Wang H., Ouyang Z., Wang L., Application of the shooting method to second-order multi-point integral boundary-value problems, Boundary Value Problems, 2013(205), 1–10, 2013.
- Wang H., Ouyang Z., Tang H., A note on the shooting method and its applications in the Stieltjes integral boundary value problems, Boundary Value Problems, 2015(102), 1–11, 2015.
- Kwong M.K., Wong J.S.W., The shooting method and nonhomogeneous multipoint BVPs of second-order ODE, Boundary Value Problems, 2007(064012), 1–16, 2007.
- Granas A., Guenther R.B., Lee J.W., The shooting method for the numerical solution of a class of nonlinear boundary value problems, SIAM Journal on Numerical Analysis, 16(5), 828–836, 1979.
- Russell R.D., Shampine L.F., Numerical methods for singular boundary value problems, SIAM Journal on Numerical Analysis, 12(1), 13–36, 1975.
- Sabeh Z., Shamsi M., Navon I.M., An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation, International Journal for Numerical Methods in Fluids, 86(7), 433–453, 2018.
- Burden R.L., Faires J.D., Numerical Analysis, 9th Edt., Brooks/Cole Publishing Company, USA, 1998.
- Abbasbandy S., Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method, Applied Mathematics and Computation, 145(2–3), 887–893, 2003.
- Noor K.I., Noor M.A., Iterative methods with fourth-order convergence for nonlinear equations, Applied Mathematics and Computation, 189(1), 221–227, 2007.
- Chun C., A new iterative method for solving nonlinear equations, Applied Mathematics and Computation, 178(2), 415–422, 2006.
- Noor M.A., Ahmad F., Javeed S., Two-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 181(2), 1068–1075, 2006.
- Argyros I., Computational Theory of Iterative Methods, 1–504, Elsevier, New York, USA, 2007.
- Kou J., The improvements of modified Newton’s method, Applied Mathematics and Computation, 189(1), 602–609, 2007.
- Liu L., Wang X., Eighth-order methods with high efficiency index for solving nonlinear equations, Applied Mathematics and Computation, 215(9), 3449–3454, 2010.
- Aziz R.C., Hashim I., Alomari A.K., Thin film flow and heat transfer on an unsteady stretching sheet with internal heating, Meccanica, 46(2), 349–357, 2011.
- Anjali Devi S.P., Raj J.W.S., Numerical simulation of magnetohydrodynamic forced convective boundary layer flow past a stretching/shrinking sheet prescribed with variable heat flux in the presence of heat source and constant suction, Journal of Applied Fluid Mechanics, 7(3), 415–423, 2014.
- Shah F.A., Noor M.A., Waseem M., Some second-derivative-free sixth-order convergent iterative methods for nonlinear equations, Maejo International Journal of Science and Technology, 10(1), 79–87, 2016.
- Selvakumar K., A computational procedure for solving singular perturbation problems arising in control system using shooting method, International Journal of Computational Science and Mathematics, 3(1), 1–10, 2011.
DOI: https://doi.org/10.2478/ijmce-2024-0013 | Journal eISSN: 2956-7068
Language: English
Page range: 165 - 178
Submitted on: Jun 10, 2023
Accepted on: Sep 3, 2023
Published on: Jan 10, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Related subjects:
© 2024 Shumaila Javeed, Evren Hincal, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.