Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem
Abstract
A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.
Dates
- Submission Date2012-08-26
- Revision Date2013-05-30
- Acceptance Date2013-05-30
- Online Date2013-06-16
References
- Widder, D. V., The heat equation, (Academic Press, New York, 1976).
- 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.
- Linz, P., Analytical and numerical methods for Volterra equations, (Philadelphia, Siam, 1985).
- Dehghan, M., The one-dimensional heat equation subject to a boundary integral specification, Chaos, Solitons, Fractals, 32(2007), 2, pp. 661-675.
- Ioannou, Y., Fyrillas, M. M., Doumanidis, C., 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.
- 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.
- Abbasbandy, S., The application of homotopy analysis method to nonlinear equations arising in heat transfer, Physics Letters A, 360(2006), 1, pp. 109-113.
- Joneidi, A. A., Ganji, D. D., Babaelahi, M., 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.
- Simões, N., Tadeu, A., António, J., Mansur, W., 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.
- 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.
- Hristov, J., Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Science, 14 (2010), 2, pp. 291-316.
- Hristov, J., Starting radial subdiffusion from a central point through a diverging medium (a sphere): heat-balance integral method, Thermal Science, 15 (2011), 1, pp.S5-S20.
- 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.
- 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
- Hetmaniok, E., Kaczmarek, K., Słota, D., Wituła, R., Zielonka, A., 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.
- Torvattanabun, M., Koonprasert, S., Duangpithak, S., 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.
- Wu, G. C., Lee, E. W. M., Fractional variational iteration method and its application, Physics Letters A, 374(2010), 25, pp.2506-2509.
- Yang, X.J., Local Fractional Functional Analysis and Its Applications, (Asian Academic publisher Limited, Hong Kong, 2011).
- Yang, X.J., Local fractional integral transforms, Progress in Nonlinear Science, 4 (2011), pp.1-225.
- Yang, X.J., Advanced Local Fractional Calculus and Its Applications, (World Science Publisher, New York, 2012).
- Yang, X,J., Baleanu,D., Fractal heat conduction problem solved by local fractional variation iteration method, Thermal Science, 17 (2013),2, pp.625-628.
- Yang, Y,J., Baleanu, D., Yang, X.J., A local fractional variational iteration method for Laplace equation within local fractional operators, Abstract and Applied Analysis, 2013 (2013), Article ID 202650.
- Su, W.H., Baleanu, D., Yang X.J., Jafari, H., 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.
- 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.
- 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.
- Khuri, S. A., Sayfy, A., A Laplace variational iteration strategy for the solution of differential equations, Applied Mathematics Letters, 25(2012), 12, pp.2298-2305.
- Wu, G. C., Baleanu, D., Variational iteration method for fractional calculus-a universal approach by Laplace transform, Advances in Difference Equations, 2013 (1), pp.1-9.
- Hu, M.S., Agarwal, R.P., Yang, X.J., Local fractional Fourier series with application to wave equation in fractal vibrating string, Abstract and Applied Analysis, 2012 (2012), Article ID 567401.
- He, J. -H., Asymptotic methods for solitary solutions and compactons, Abstract and Applied Analysis, 2012 (2012), Article ID 916793.
Volume
17,
Issue
3,
Pages715 -721