Abstract
References
- [1] King A.C. Billingham J. and Otto S.R., Differential Equations: Linear, Nonlinear, Ordinary, Partial. Cambridge University Press, New York, (2003). [2] Filobello-Nino U., Vazquez-Leal H., Boubaker K., Khan Y., Perz-Sesma A., Sarmiento-Reyes A., Jimenez-Fernandez V.M., Diaz-Sanchez A., Herrera-May A., Sanchez-Orea J. and Pereyra-Castro K. (2013). Perturbation Method as a Powerful Tool to Solve Highly Nonlinear Problems: The Case of Gelfand’s Equation, Asian J. Math. Stat. vol.6(2)76, 2013. [3] Zarebnia M. and Hoshyar M., Solution of Bratu-Type Equation Via Spline Method, Acta Universitatis Apulensis, (37) 61-72, 2014. [4] Abdelmajid El hajaji, Khalid Hilal, El merzguioui Mohamed, and Elghordaf Jalila, A Cubic Spline Collocation Method for Solving Bratu’s Problem, IISTE J. Mathematical Theory, and Modeling, 3(14), 2013. [5] Jain M.K., Iyengar S.R.K. and Jain R.K., Numerical Methods for Scientific and Engineering Computation, Sixth Edition, New Age International Publishers, (Formerly Wiley Eastern Limited), New Delhi.,2007. [6] Batiha B., Numerical Solution of Bratu-Type Equations by the Variational Iteration Method, Hacettepe J. Math. Stat., 39(1), 23-29, 2010. [7] Aksoy Y, Pakdemirli M., New perturbation–iteration solutions for Bratu-type equations. Computers & Mathematics with Applications, 59(8), 2802-2808, 2010. [8] Duan JS, Rach R, Baleanu D, Wazwaz AM., A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in Fractional Calculus.3(2),73-99, 2012. [9] Moradi E, Babolian E, Javadi S., The explicit formulas for reproducing kernel of some Hilbert spaces, Miskolc Mathematical Notes, 16(2), 1041-1053, 2015. [10] Darwish MA, Kashkari BS., Numerical solutions of second-order initial value problems of Bratu-type via optimal homotopy asymptotic method, American Journal of Computational Mathematics, 4(2):47, 2014.
Numerical Solutions of Second Order Initial Value Problems of Bratu-Type Equations using Predictor-Corrector Method
Abstract
In this paper, numerical solutions of second-order initial value problems of Bratu-type equation using the predictor-corrector method is considered. The stability and convergence of the proposed method are proved. To validate the applicability of the scheme, two model problems are considered for numerical experimentation. The numerical results are tabulated in terms of maximum absolute errors and it is observed that the present method is more accurate and convergent and it also improves the results of the methods existing in the literature.
Keywords
Predictor-corrector method Initial value problem quasi linearization method Bratu-Type equation
References
- [1] King A.C. Billingham J. and Otto S.R., Differential Equations: Linear, Nonlinear, Ordinary, Partial. Cambridge University Press, New York, (2003). [2] Filobello-Nino U., Vazquez-Leal H., Boubaker K., Khan Y., Perz-Sesma A., Sarmiento-Reyes A., Jimenez-Fernandez V.M., Diaz-Sanchez A., Herrera-May A., Sanchez-Orea J. and Pereyra-Castro K. (2013). Perturbation Method as a Powerful Tool to Solve Highly Nonlinear Problems: The Case of Gelfand’s Equation, Asian J. Math. Stat. vol.6(2)76, 2013. [3] Zarebnia M. and Hoshyar M., Solution of Bratu-Type Equation Via Spline Method, Acta Universitatis Apulensis, (37) 61-72, 2014. [4] Abdelmajid El hajaji, Khalid Hilal, El merzguioui Mohamed, and Elghordaf Jalila, A Cubic Spline Collocation Method for Solving Bratu’s Problem, IISTE J. Mathematical Theory, and Modeling, 3(14), 2013. [5] Jain M.K., Iyengar S.R.K. and Jain R.K., Numerical Methods for Scientific and Engineering Computation, Sixth Edition, New Age International Publishers, (Formerly Wiley Eastern Limited), New Delhi.,2007. [6] Batiha B., Numerical Solution of Bratu-Type Equations by the Variational Iteration Method, Hacettepe J. Math. Stat., 39(1), 23-29, 2010. [7] Aksoy Y, Pakdemirli M., New perturbation–iteration solutions for Bratu-type equations. Computers & Mathematics with Applications, 59(8), 2802-2808, 2010. [8] Duan JS, Rach R, Baleanu D, Wazwaz AM., A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in Fractional Calculus.3(2),73-99, 2012. [9] Moradi E, Babolian E, Javadi S., The explicit formulas for reproducing kernel of some Hilbert spaces, Miskolc Mathematical Notes, 16(2), 1041-1053, 2015. [10] Darwish MA, Kashkari BS., Numerical solutions of second-order initial value problems of Bratu-type via optimal homotopy asymptotic method, American Journal of Computational Mathematics, 4(2):47, 2014.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 3, 2020 |
| Acceptance Date | April 23, 2020 |
| Published in Issue | Year 2020 Volume: 12 Issue: 1 |
