Variational homotopy perturbation method for solving higher dimensional initial boundary value problems

Mathematical Problems in Engineering

Volumn 2008, Issue , 2008, Pages

  Noor, Muhammad Aslam ^a   Mohyud Din, Syed Tauseef ^a  

^a Department of Electrical Computer Engineering   (Pakistan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; INITIAL VALUE PROBLEMS; PERTURBATION TECHNIQUES;

HOMOTOPY PERTURBATION METHOD (HPM); INITIAL BOUNDARY VALUE PROBLEM (IBVP); ROUND-OFF ERRORS; VARIABLE COEFFICIENTS; VARIATIONAL ITERATION METHOD (VIM);

ITERATIVE METHODS;

EID: 47649131065     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2008/696734     Document Type: Article

References (32)

1. Miller W. Jr., Symmetries of differential equations. The hypergeometric and Euler-Darboux equations SIAM Journal on Mathematical Analysis 1973 4 2 314 328
2. Wilcox R., Closed-form solution of the differential equation ((2/xy)+ax(/x)+by(/y)+cxy+(/t))P=0 by normal-ordering exponential operators Journal of Mathematical Physics 1970 11 1235 1237
3. Manwell A. R., The Tricomi Equation with Applications to the Theory of Plane Transonic Flow 1979 35 London, UK Pitman vi+185 Research Notes in Mathematics
4. Nirmala N., Vedan M. J., Baby B. V., A variable coefficient Korteweg-de Vries equation: similarity analysis and exact solutionII Journal of Mathematical Physics 1986 27 11 2644 2646
5. Iyanaga S., Kawada Y., Encyclopedic Dictionary of Mathematics 1962 Cambridge, Mass, USA MIT Press
6. Soliman A. A., A numerical simulation and explicit solutions of KdV-Burgers and Laxs seventh-order KdV equations Chaos, Solitons Fractals 2006 29 2 294 302
7. Wazwaz A.-M., The decomposition method for solving higher dimensional initial boundary value problems of variable coefficients International Journal of Computer Mathematics 2000 76 2 159 172
8. He J.-H., Some asymptotic methods for strongly nonlinear equations International Journal of Modern Physics B 2006 20 10 1141 1199
9. He J.-H., Homotopy perturbation technique Computer Methods in Applied Mechanics and Engineering 1999 178 3-4 257 262
10. He J.-H., Homotopy perturbation method for solving boundary value problems Physics Letters A 2006 350 1-2 87 88
11. He J.-H., Comparison of homotopy perturbation method and homotopy analysis method Applied Mathematics and Computation 2004 156 2 527 539
12. He J.-H., Homotopy perturbation method for bifurcation of nonlinear problems International Journal of Nonlinear Sciences and Numerical Simulation 2005 6 2 207 208
13. He J.-H., The homotopy perturbation method nonlinear oscillators with discontinuities Applied Mathematics and Computation 2004 151 1 287 292
14. He J.-H., A coupling method of a homotopy technique and a perturbation technique for non-linear problems International Journal of Non-Linear Mechanics 2000 35 1 37 43
15. He J.-H., Variational iteration methoda kind of non-linear analytical technique: some examples International Journal of Non-Linear Mechanics 1999 34 4 699 708
16. He J.-H., Variational iteration method for autonomous ordinary differential systems Applied Mathematics and Computation 2000 114 2-3 115 123
17. He J.-H., Wu X.-H., Construction of solitary solution and compacton-like solution by variational iteration method Chaos, Solitons Fractals 2006 29 1 108 113
18. He J.-H., Wu X.-H., Variational iteration method: new development and applications Computers Mathematics with Applications 2007 54 7-8 881 894
19. Inokuti M., Sekine H., Mura T., Nemat-Naseer S., General use of the Lagrange multiplier in nonlinear mathematical physics Variational Method in the Mechanics of Solids 1978 New York, NY, USA Pergamon Press 156 162
20. Noor M. A., Mohyud-Din S. T., Variational iteration decomposition method for solving higher dimensional initial boundary value problems with variable coefficients. preprint, 2007
21. Mohyud-Din S. T., A reliable algorithm for Blasius equation Proceedings of the International Conference of Mathematical Sciences (ICMS 07) November 2007 Selangor, Malaysia 616 626
22. Noor M. A., Mohyud-Din S. T., Variational iteration technique for solving higher order boundary value problems Applied Mathematics and Computation 2007 189 2 1929 1942
23. Noor M. A., Mohyud-Din S. T., An efficient method for fourth-order boundary value propblems Computers Mathematics with Applications 2007 54 7-8 1101 1111
24. Noor M. A., Mohyud-Din S. T., Variational iteration technique for solving higher order boundary value problems Applied Mathematics and Computation 2007 189 2 1929 1942
25. Noor M. A., Mohyud-Din S. T., Variational iteration decomposition method for solving eighth-order boundary value problems Differential Equations and Nonlinear Mechanics 2007 2007 16
26. Mohyud-Din S. T., Noor M. A., Homotopy perturbation method for solving fourth order boundary value problems Mathematical Problems in Engineering 2006 2006 15
27. Noor M. A., Mohyud-Din S. T., Homotopy method for solving eighth order boundary value problems Journal of Mathematical Analysis and Approximation Theory 2006 1 2 161 169
28. Noor M. A., Mohyud-Din S. T., An efficient algorithm for solving fifth-order boundary value problems Mathematical and Computer Modelling 2007 45 7-8 954 964
29. Noor M. A.
30. Noor M. A., Mohyud-Din S. T., A reliable approach for solving linear and nonlinear sixth-order boundary value problems International Journal of Computational and Applied Mathematics 2007 2 2 163 172
31. Noor M. A., Mohyud-Din S. T., Approximate solutions of Flieral-Petviashivili equation and its variants International Journal of Mathematics and Computer Science 2007 2 4 345 360
32. Noor M. A., On iterative methods for nonlinear equations using homotopy perturbation technique. preprint, 2008