×

An iterative method for solving nonlinear functional equations. (English) Zbl 1087.65055

Summary: An iterative method for solving nonlinear functional equations, viz. nonlinear Volterra integral equations, algebraic equations and systems of ordinary differential equation, nonlinear algebraic equations and fractional differential equations is discussed.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
45G10 Other nonlinear integral equations
65R20 Numerical methods for integral equations
65H10 Numerical computation of solutions to systems of equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer Acad. Publ. · Zbl 0802.65122
[2] Babolian, E.; Biazar, J.; Vahidi, A. R., Solution of a system of nonlinear equations by Adomian decomposition method, J. Math. Anal. Appl., 150, 847-854 (2004) · Zbl 1075.65073
[3] Biazar, J.; Babolian, E.; Islam, R., Solution of the system of ordinary differential equations by Adomian decomposition method, Appl. Math. Comput., 147, 713-719 (2004) · Zbl 1034.65053
[4] Biazar, J.; Babolian, E.; Islam, R., Solution of the system of Volterra integral equations of the first kind by Adomian decomposition method, Appl. Math. Comput., 139, 249-258 (2003) · Zbl 1027.65180
[5] Cherruault, Y., Convergence of Adomian’s method, Kybernetes, 8, 31-38 (1988) · Zbl 0697.65051
[6] Daftardar-Gejji, V.; Jafari, H., Adomian decomposition: a tool for solving a system of fractional differential equations, J. Math. Anal. Appl., 301, 508-518 (2005) · Zbl 1061.34003
[7] El-Sayed, S. M., The modified decomposition method for solving nonlinear algebraic equations, Appl. Math. Comput., 132, 589-597 (2002) · Zbl 1031.65067
[8] H. Jafari, V. Daftardar-Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations, submitted for publication; H. Jafari, V. Daftardar-Gejji, Revised Adomian decomposition method for solving a system of nonlinear equations, submitted for publication · Zbl 1088.65047
[9] H. Jafari, V. Daftardar-Gejji, Solving system of nonlinear fractional differential equations, submitted for publication; H. Jafari, V. Daftardar-Gejji, Solving system of nonlinear fractional differential equations, submitted for publication · Zbl 1099.65137
[10] Jerri, A. J., Introduction to Integral Equations with Applications (1999), Wiley-Interscience · Zbl 0938.45001
[11] Ouedraogo, R. Z.; Cherruault, Y.; Abbaoui, K., Convergence of Adomian’s decomposition method applied to algebraic equations, Kybernetes, 29, 1298-1305 (2000) · Zbl 0994.65054
[12] Podlubny, I., Fractional Differential Equations (1999), Academic Press · Zbl 0918.34010
[13] Wazwaz, A., A First Course in Integral Equations (1997), World Scientific · Zbl 0924.45001
[14] Wazwaz, A., A reliable modification of Adomian decomposition method, Appl. Math. Comput., 102, 77-86 (1999) · Zbl 0928.65083
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.