An iterative method for solving boundary value problems for second order differential equations
DOI:
https://doi.org/10.24297/jam.v12i8.4911Keywords:
Second-order differential equation, Robin boundary conditions, Fixed-Point theorem, Fredholm operator, ADMAbstract
The purpose of this paper is to investigate the application of the Adomian decomposition method (ADM) for solving boundary value problems for second-order differential equations with Robin boundary conditions. We first reformulate the boundary value problems for linear equations as a fixed point problems for a linear Fredholm integral operator, and then apply the ADM. We also extend our approach to include second-order nonlinear differential equations subject Robin boundary conditions.Downloads
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References
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[2] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers:
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[9] Duan J., Rach R., A new modification of the Adomian decomposition method for solving boundary value problems for
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equations, Appl. Math. Comput. 2011; 217:8907-8913.
[11] Bougoffa L., Rach R., Mennouni A., A convenient technique for solving linear and nonlinear Abel integral equations
by the Adomian decomposition method, Appl. Math. Comput. 2011; 218:1785-1793.
[12] Bougoffa L., Al-Haqbani M., Rach R., A convenient technique for solving integral equations of the first kind by the
Adomian decomposition method, Kybernetes 2012; 41:145-156.
[13] Duana J., Rach R., A new modification of the Adomian decomposition method for solving boundary value problems
for higher order nonlinear differential equations, Appl. Math. Comput. 2011; 218: 4090-4118.
[14] Abdul-Majid Wazwaz, R. Rach and L. Bougoffa, Dual solutions for nonlinear boundary value problems by the
Adomian decomposition method,International Journal of Numerical Methods for Heat and Fluid Flow, In press Volume 26,
Issue 8, (2016).
[2] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers:
Dordrecht, 1989.
[3] Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic: Dordrecht, 1994.
[4] Adomian G., Rach R., Transformation of series,Appl. Math. Lett. 1999; 4:69-71.
[5] Adomian G., Rach R., Meyers RE., A modified decomposition,Comput. Math. with Appl. 1999; 23:17-23.
[6] Adomian G., Rach R., Inhomogeneous nonlinear partial differential equations with variable coefficients, Appl. Math.
Lett. 1992; 5:11-12.
[7] Adomian G., Rach R., Nonlinear transformation of series – part II, Comput. Math. Appl. 1992; 23:79-83.
[8] Wazwaz AM., Partial Differential Equations and Solitary Waves Theory, Higher Education Press and Springer: Beijing
and Berlin, 2009.
[9] Duan J., Rach R., A new modification of the Adomian decomposition method for solving boundary value problems for
higher order nonlinear differential equations, Appl. Math. Comput. 2011; 218:4090-4118.
[10] Bougoffa L., Rach R., Mennouni A. An approximate method for solving a class of weakly-singular Volterra integrodifferential
equations, Appl. Math. Comput. 2011; 217:8907-8913.
[11] Bougoffa L., Rach R., Mennouni A., A convenient technique for solving linear and nonlinear Abel integral equations
by the Adomian decomposition method, Appl. Math. Comput. 2011; 218:1785-1793.
[12] Bougoffa L., Al-Haqbani M., Rach R., A convenient technique for solving integral equations of the first kind by the
Adomian decomposition method, Kybernetes 2012; 41:145-156.
[13] Duana J., Rach R., A new modification of the Adomian decomposition method for solving boundary value problems
for higher order nonlinear differential equations, Appl. Math. Comput. 2011; 218: 4090-4118.
[14] Abdul-Majid Wazwaz, R. Rach and L. Bougoffa, Dual solutions for nonlinear boundary value problems by the
Adomian decomposition method,International Journal of Numerical Methods for Heat and Fluid Flow, In press Volume 26,
Issue 8, (2016).
Published
2016-09-15
How to Cite
Alruwaily, Y. S. (2016). An iterative method for solving boundary value problems for second order differential equations. JOURNAL OF ADVANCES IN MATHEMATICS, 12(8), 6489–6499. https://doi.org/10.24297/jam.v12i8.4911
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