An algorithm for solving the fractional convection-diffusion equation with nonlinear source term

Communications in Nonlinear Science and Numerical Simulation

Volumn 12, Issue 7, 2007, Pages 1283-1290

  Momani, Shaher ^a  

^a MUTAH UNIVERSITY   (Jordan)

Author keywords

Caputo fractional derivative; Convection diffusion equation; Decomposition method

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; NONLINEAR EQUATIONS;

ADOMIAN DECOMPOSITION METHOD; CAPUTO FRACTIONAL DERIVATIVE; CONVECTION-DIFFUSION EQUATION;

DOMAIN DECOMPOSITION METHODS;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; DOMAIN DECOMPOSITION METHODS; NONLINEAR EQUATIONS;

EID: 34047158626     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2005.12.007     Document Type: Article

References (22)

1. Mainardi F. Fractional calculus: Some basic problems in continuum and statistical mechanics. In: Carpinteri A., and Mainardi F. (Eds). Fractals and fractional calculus in continuum mechanics (1997), Springer-Verlag, New York
2. Podlubny I. Fractional differential equations (1999), Academic Press, New York
3. Miller K.S., and Ross B. An introduction to the fractional calculus and fractional differential equations (1993), John Wiley & Sons, New York
4. Samko G., Kilbas A.A., and Marichev O.I. Fractional integrals and derivatives: theory and applications (1993), Gordon and Breach, Yverdon
5. Luchko Y., and Srivastava H.M. The exact solution of certain differential equations of fractional order by using operational calculus. Comp Math Appl 9 (1995) 73-85
6. Luchko A., and Gorenflo R. The initial value problem for some fractional differential equations with the Caputo derivative, Preprint series A08-98 (1998), Fachbreich Mathematik und Informatik, Freic Universitat Berlin
7. Momani S., and Al-Khaled K. Numerical solutions for systems of fractional differential equations by the decomposition method. Appl Math Comput 162 3 (2005) 1351-1365
8. Shawagfeh N.T. Analytical approximate solutions for nonlinear fractional differential equations. Appl Math Comput 131 2 (2002) 517-529
9. Diethelm K., and Ford N.J. Multi-order fractional differential equations and their numerical solution. Appl Math Comput 154 (2004) 621-640
10. Edwards J.T., Ford N.J., and Simpson A.C. The numerical solution of linear multi-term fractional differential equations: systems of equations. J Comput Appl Math 148 (2002) 401-418
11. Al-Khaled K., and Momani S. An approximate solution for a fractional diffusion-wave equation using the decomposition method. Appl Math Comput 165 2 (2005) 473-483
12. Momani S. Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method. Appl Math Comput 165 2 (2002) 459-472
13. Adomian G. A review of the decomposition method in applied mathematics. J Math Anal Appl 135 (1988) 501-544
14. Adomian G. Solving frontier problems of physics: the decomposition method (1994), Kluwer Academic Publishers, Boston
15. Sincovec R.F., and Madsen N.K. Software for non-linear partial differential equations. ACM Trans Math Software (1975)
16. Inc M., and Cherruault Y. A new approach to solve a diffusion-convection problem. Kybernetes 31 (2002) 536-549
17. Wazwaz A.M. A reliable modification of Adomian's decomposition method. Appl Math Comput 92 (1998) 1-7
18. Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J Roy Astrol Soc 13 (1967) 529-539
19. Diethelm K., Ford N.J., Freed A.D., and Luchko Y. Algorithms for the fractional calculus: a selection of numerical methods. Comp Methods Appl Mech Eng 194 (2005) 743-773
20. Podlubny I. Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calculus Appl Anal 5 (2002) 367-386
21. Cherruault Y. Convergence of Adomian's method. Kybernetes 18 (1989) 31-38
22. Cherruault Y., and Adomian G. Decomposition methods: a new proof of convergence. Math Comput Modell 18 (1993) 103-106