Reconstructive schemes for variational iteration method within yang-laplace transform with application to fractal heat conduction problem

Thermal Science

Volumn 17, Issue 3, 2013, Pages 715-721

  Liu, Chun Feng ^a   Kong, Shan Shan ^b   Yuan, Shu Juan ^a  

^a HEBEI UNITED UNIVERSITY   (China)

^b BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Fractal heat conduction equation; Local fractional derivative; Local fractional variational iteration method; Yang Laplace transform

Indexed keywords

FRACTALS; HEAT CONDUCTION; ITERATIVE METHODS; LAGRANGE MULTIPLIERS;

COMPACT SOLUTIONS; FRACTAL HEAT CONDUCTION EQUATION; HEAT CONDUCTION EQUATIONS; HEAT CONDUCTION PROBLEMS; HIGH-ACCURACY; LOCAL FRACTIONAL DERIVATIVES; LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD; VARIATIONAL ITERATION METHOD; YANG-LAPLACE TRANSFORM;

LAPLACE TRANSFORMS;

EID: 84884850577     PISSN: 03549836     EISSN: None     Source Type: Journal    
DOI: 10.2298/TSCI120826075L     Document Type: Article

References (29)

1. Widder, D. V., The Heat Equation, Academic Press, New York, USA, 1976
2. Hsiao, G., MacCamy, R. C., Solution of Boundary Value Problems by Integral Equations of the First Kind, SIAM Review, 15 (1973), 4, pp. 687-705
3. Linz, P., Analytical and Numerical Methods for Volterra Equations, Siam, Philadelphia, Penn., USA, 1985
4. Dehghan, M., The One-Dimensional Heat Equation Subject to a Boundary Integral Specification, Chaos, Solitons, Fractals, 32 (2007), 2, pp. 661-675
5. Ioannou, Y., et al., Approximate Solution to Fredholm Integral Equations Using Linear Regression and Applications to Heat and Mass Transfer, Engineering Analysis with Boundary Elements, 36 (2012), 8, pp. 1278-1283
6. Nadeem, S., Akbar, N. S., Effects of Heat Transfer on the Peristaltic Transport of MHD Newtonian Fluid with Variable Viscosity: Application of Adomian Decomposition Method, Communications in Nonlinear Science and Numerical Simulation, 14 (2009),11, pp. 3844-3855
7. Abbasbandy, S., The Application of Homotopy Analysis Method to Nonlinear Equations Arising in Heat Transfer, Physics Letters A, 360 (2006), 1, pp. 109-113
8. Joneidi, A. A., et al., Differential Transformation Method to Determine Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity, International Communications in Heat and Mass Transfer, 36 (2009), 7, pp. 757-762
9. Simoes, N., et al., Transient Heat Conduction under Nonzero Initial Conditions: A Solution Using the Boundary Element Method in the Frequency Domain, Engineering Analysis with Boundary Elements, 36 (2012), 4, pp. 562-567
10. Hristov, J., Approximate Solutions to Fractional Sub-Diffusion Equations: The Heat-Balance Integral Method, The European Physical Journal Special Topics, 193 (2011), 4, pp. 229-243
11. Hristov, J., Heat-Balance Integral to Fractional (Half-Time) Heat Diffusion Sub-Model, Thermal Science, 14 (2010), 2, pp. 291-316
12. Hristov, J., Starting Radial Subdiffusion from a Central Point through a Diverging Medium (a Sphere): Heat-Balance Integral Method, Thermal Science, 15 (2011), Suppl. 1, pp. S5-S20
13. He, J.-H., Variational Iteration Method-a Kind of Non-Linear Analytical Technique: Some Examples, International Journal of Non-Linear Mechanics, 34 (1999), 4, pp. 699-708
14. Hristov, J., An Exercise with the He's Variation Iteration Method to a Fractional Bernoulli Equation Arising in Transient Conduction with Non-Linear Heat Flux at the Boundary, International Review of Chemical Engineering, 4 (2012), 5, pp. 489-497
15. Hetmaniok, E., et al., Application of the Variational Iteration Method for Determining the Temperature in the Heterogeneous Casting-Mould System, International Review of Chemical Engineering, 4 (2012), 5, pp. 511-515
16. Torvattanabun, M., et al., Efficacy of Variational Iteration Method for Nonlinear Heat Transfer Equations-Classical and Multistage Approach, International Review of Chemical Engineering, 4 (2012), 5, pp. 524-528
17. Wu, G. C., Lee, E. W. M., Fractional Variational Iteration Method and its Application, Physics Letters A, 374 (2010), 25, pp. 2506-2509
18. Yang, X. J., Local Fractional Functional Analysis and Its Applications, Asian Academic Publisher Limited, Hong Kong, 2011
19. Yang, X. J., Local Fractional Integral Transforms, Progress in Nonlinear Science, 4 (2011), pp. 1-225
20. Yang, X. J., Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, 2012
21. Yang, X. J., Baleanu, D., Fractal Heat Conduction Problem Solved by Local Fractional Variation Iteration Method, Thermal Science, 17 (2013), 2, pp. 625-628
22. Yang, Y. J., et al., A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators, Abstract and Applied Analysis, 2013 (2013), Article ID 202650
23. Su,W. H., et al., Damped Wave Equation and Dissipative Wave Equation in Fractal Strings within the Local Fractional Variational Iteration Method, Fixed Point Theory and Applications, 2013 (2013), 1, pp. 89-102
24. He, J.-H., Liu, F.-J., Local Fractional Variational Iteration Method for Fractal Heat Transfer in Silk Cocoon Hierarchy, Nonlinear Science Letters A, 4 (2013), 1, pp. 15-20
25. Hesameddini, E., Latifizadeh, H., Reconstruction of Variational Iteration Algorithms Using the Laplace Transform, International Journal of Nonlinear Sciences and Numerical Simulation, 10 (2009), 11-12, pp. 1377-1382
26. Khuri, S. A., Sayfy, A., ALaplace Variational Iteration Strategy for the Solution of Differential Equations, Applied Mathematics Letters, 25 (2012), 12, pp. 2298-2305
27. Wu, G. C., Baleanu, D., Variational Iteration Method for Fractional Calculus-an Universal Approach by Laplace Transform, Advances in Difference Equations, 2013 (2013), 1, pp.1-9
28. Hu, M. S., et al., Local Fractional Fourier Series with Application to wave Equation in Fractal Vibrating String, Abstract and Applied Analysis, 2012 (2012), Article ID 567401
29. He, J.-H., Asymptotic Methods for Solitary Solutions and Compactons, Abstract and Applied Analysis, 2012 (2012), Article ID 916793