Analytical solutions of boundary values problem of 2D and 3D poisson and biharmonic equations by homotopy decomposition method

Abstract and Applied Analysis

Volumn 2013, Issue , 2013, Pages

  Atangana, Abdon ^a   Klçman, Adem ^b  

^a UNIVERSITY OF THE FREE STATE   (South Africa)

^b UNIVERSITY PUTRA MALAYSIA   (Malaysia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84885626980     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2013/380484     Document Type: Article

References (26)

1. Mittal R. C., Gahlaut S., High-order finite-difference schemes to solve Poisson's equation in polar coordinates. IMA Journal of Numerical Analysis 1991 11 2 261 270 10.1093/imanum/11.2.261 MR1105230
2. Perrey-Debain E., ter Morsche H. G., B-spline approximation and fast wavelet transform for an efficient evaluation of particular solutions for Poisson's equation. Engineering Analysis with Boundary Elements 2002 26 1 1 13 (Pubitemid 33034370)
3. Sutmann G., Steffen B., High-order compact solvers for the three-dimensional Poisson equation. Journal of Computational and Applied Mathematics 2006 187 2 142 170 10.1016/j.cam.2005.03.041 MR2185666 ZBL1081.65099 (Pubitemid 41586510)
4. Ge Y., Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation. Journal of Computational Physics 2010 229 18 6381 6391 10.1016/j.jcp.2010.04.048 MR2660310 ZBL1197.65169
5. Gumerov N. A., Duraiswami R., Fast multipole method for the biharmonic equation in three dimensions. Journal of Computational Physics 2006 215 1 363 383 10.1016/j.jcp.2005.10.029 MR2215660 ZBL1103.65122 (Pubitemid 43695594)
6. Khattar D., Singh S., Mohanty R. K., A new coupled approach high accuracy numerical method for the solution of 3D non-linear biharmonic equations. Applied Mathematics and Computation 2009 215 8 3036 3044 10.1016/j.amc.2009.09. 052 MR2563420 ZBL1180.65137
7. Altas I., Erhel J., Gupta M. M., High accuracy solution of three-dimensional biharmonic equations. Numerical Algorithms 2002 29 1-3 1 19 10.1023/A:1014866618680 MR1896942 ZBL0992.65115 (Pubitemid 37132312)
8. Jeon Y., New indirect scalar boundary integral equation formulas for the biharmonic equation. Journal of Computational and Applied Mathematics 2001 135 2 313 324 10.1016/S0377-0427(00)00590-2 MR1850546 ZBL0986.31003 (Pubitemid 32901676)
9. Mai-Duy N., Tanner R. I., A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. Journal of Computational and Applied Mathematics 2007 201 1 30 47 10.1016/j.cam.2006.01.030 MR2293536 ZBL1110.65112 (Pubitemid 46080576)
10. Mai-Duy N., Tran-Cong T., Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks. Engineering Analysis with Boundary Elements 2006 30 2 77 87 (Pubitemid 43120303)
11. Mai-Duy N., Tanner R. I., An effective high order interpolation scheme in BIEM for biharmonic boundary value problems. Engineering Analysis with Boundary Elements 2005 29 3 210 223 (Pubitemid 40424037)
12. Li X., Zhu J., A Galerkin boundary node method for biharmonic problems. Engineering Analysis with Boundary Elements 2009 33 6 858 865 10.1016/j.enganabound.2008.11.002 MR2496790 ZBL1244.65175
13. Mai-Duy N., See H., Tran-Cong T., A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains. Applied Mathematical Modelling 2009 33 1 284 299 10.1016/j.apm.2007.11. 002 MR2458511 ZBL1167.65454
14. Dissanayake M. W. M. G., Phan-Thien N., Neural-network-based approximations for solving partial differential equations. communications in Numerical Methods in Engineering 1994 10 3 195 201
15. Mai-Duy N., Tanner R. I., A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs. International Journal of Numerical Methods for Heat & Fluid Flow 2007 17 2 165 186 10.1108/09615530710723948 MR2317041 ZBL1231.76188 (Pubitemid 46181196)
16. Shi Z., Cao Y.-Y., Chen Q.-J., Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method. Applied Mathematical Modelling 2012 36 11 5143 5161 10.1016/j.apm.2011.11.078 MR2956733 ZBL1254.65138
17. Atangana A., Botha J. F., Analytical solution of the ground water flow equation obtained via homotopy decomposition method. Journal of Earth Science & Climatic Change 2012 3 115 10. 4172/2157-7617.1000115
18. Atangana A., Secer A., The time-fractional coupled-Korteweg-de-Vries equations. Abstract and Applied Analysis 2013 2013 8 947986 MR3035318 10.1155/2013/947986
19. Atangana A., Ahmed A., A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of non-integer derivatives. Abstract Applied Analysisaccepted 2013 2013 9 671321 10.1155/2013/671321
20. + cells and attractor one-dimensional Keller-Segel equations. Advance in Difference Equation 2013 2013 94 10.1186/1687-1847-2013-94
21. Mohyud-Din S. T., Yildirim A., Hosseini M. M., Variational iteration method for initial and boundary value problems using He's polynomials. International Journal of Differential Equations 2010 2010 28 426213 MR2629625 ZBL1206.35019
22. Elbeleze A. A., Klçman A., Taib B. M., Homotopy perturbation method for fractional Black-Scholes European option pricing equations using Sumudu transform. Mathematical Problems in Engineering 2013 2013 7 524852 MR3049813 10.1155/2013/524852
23. Elbeleze A. A., Klçman A., Taib B. M., Application of homotopy perturbation and variational iteration method for Fredholm integro-differential equation of fractional order. Abstract and Applied Analysis 2012 2012 14 763139 10.1155/2012/763139
24. El-Sayed A. M. A., Hammad D., A reliable treatment of homotopy perturbation method for solving the nonlinear Klein-Gordon equation of arbitrary (fractional) orders). Journal of Applied Mathematics 2012 2012 13 581481 10.1155/2012/581481
25. Kajani M. T., Ghasemi M., Babolian E., Comparison between the homotopy perturbation method and the sine-cosine wavelet method for solving linear integro-differential equations. Computers & Mathematics with Applications 2007 54 7-8 1162 1168 10.1016/j.camwa.2006.12.062 MR2398139 ZBL1141.65397 (Pubitemid 47496211)
26. Khalifa A. K., The decomposition method for one dimensional biharmonic equations. International Journal of Simulation and Process Modelling 2006 2 1-2