An Efficient Method to Solve Thermal Wave Equation

Show more

References

[1] J. Opsal, A. Rosencwaig and D. L.Willenborg, “Thermal-Wave Detection and Thin-Film Thickness Measurements with Laser Beam Deflection,” Applied Optics, Vol. 22, No. 20, 1983, pp. 3169-3176. http://dx.doi.org/10.1364/AO.22.003169

[2] Z. Y. Yan, “Generalized Method and Its Application in the Higher-Order Nonlinear Schrodinger Equation in Nonlinear Optical Fibres,” Chaos Solitons and Fractals, Vol. 16, No. 5, 2003, pp. 759-766. http://dx.doi.org/10.1016/S0960-0779(02)00435-6

[3] J. Mei, H. Zhang and D. Jiang, “New Exact Solutions for a Reaction-Diffusion Equation and a Quasi-Camassa Holm Equation,” Applied Mathematics E-Notes, Vol. 4, 2004, pp. 85-91.

[4] E. S. Fahmy and H. A. Abdusalam, “Exact Solutions for Some Reaction Diffusion Systems with Nonlinear Reaction Polynomial Terms,” Applied Mathematical Sciences, Vol. 3, No. 11, 2009, pp. 533-540.

[5] M. S. H. Chowdhury and I. Hashim, “Analytical Solution for Cauchy Reaction-Diffusion Problems by Homotopy Perturbation Method,” Sains Malaysiana, Vol. 39, No. 3, 2010, pp. 495-504.

[6] S. Puri and K. Wiese, “Perturbative Linearization of Reaction-Diffusion Equations,” Journal of Physics A: Mathematical and General, Vol. 36, 2003, pp. 2043-2054. http://dx.doi.org/10.1088/0305-4470/36/8/303

[7] L. D. Ropp, N. J. Shadid and C. C. Ober, “Studies of the Accuracy of Time Integration Methods for Reaction-Diffusion Equations,” Journal of Computational Physics, Vol. 194, No. 2, 2004, pp. 544-574. http://dx.doi.org/10.1016/j.jcp.2003.08.033

[8] R. G. Marcus, “Finite-Difference Schemes for Reaction-Diffusion Equations Modeling Predator—Prey Interactions in MATLAB,” Bulletin of Mathematical Biology, Vol. 69, No. 3, 2007, pp. 931-956. http://dx.doi.org/10.1007/s11538-006-9062-3

[9] B. Liu, M. B. Allen, H. Kojouharov and B. Chen, “Finite-Element Solution of Reaction-Diffusion Equations with Advection,” Computational Mechanics, 1996, pp. 3-12.

[10] X. Christos and L. Oberbroeckling, “On the Finite Element Approximation of Systems of Reaction—Diffusion Equations by p/hp Methods,” Global Science, Vol. 28, No. 3, 2010, pp. 386-400.

[11] G. Meral and M. S. Tezer, “Solution of Nonlinear Reaction-Diffusion Equation by Using Dual Reciprocity Boundary Element Method with Finite Difference or Least Squares Method,” Advances in Boundary Element Techniques, 2008, pp. 317-22.

[12] C. Shu, “Differential Quadrature and Its Application in Engineering,” Springer Verlag, London, 2000.

http://dx.doi.org/10.1007/978-1-4471-0407-0

[13] T. Y. Wu and G. R. Liu, “A Differential Quadrature as a Numerical Method to Solve Differential Equations,” Computational Mechanics, Vol. 24, No. 3, 1999, pp. 197-205.

http://dx.doi.org/10.1007/s004660050452

[14] G. Meral, “Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method,” World Academy of Science, Engineering and Technology, Vol. 41, 2010, pp. 1178-1183.

[15] V. Kajal, “Numerical Solutions of Some Reaction-Diffusion Equations by Differential Quadrature Method,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 14, 2010, pp. 68-80.

[16] M. Salah, R. M. Amer and M. S. Matbuly, “The Differential Quadrature Solution of Reaction-Diffusion Equation Using Explicit and Implicit Numerical Schemes,” Applied Mathematics, 2014.

[17] C. Shu, Q. Yao and K. S. Yeo, “Block-Marching in Time with DQ Discretization: An Efficient Method for Time-Dependent Problems,” Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 41, 2002, pp. 4587-4579.

http://dx.doi.org/10.1016/S0045-7825(02)00387-0

[18] J. S. Nadjafi and A. Ghorbani, “He’s Homotopy Perturbation Method: An Effective Tool for Solving Nonlinear Integral and Integro-Differential Equations,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 2379-2390.

http://dx.doi.org/10.1016/j.camwa.2009.03.032

[19] H. S. Prasad and Y. N. Reddy, “Numerical Solution of Singularly Perturbed Differential-Difference Equations with Small Shifts of Mixed Type by Differential Quadrature Method,” American Journal of Computational and Applied Mathematics, Vol. 2, No. 1, 2012, pp. 46-52.

http://dx.doi.org/10.5923/j.ajcam.20120201.09

[20] J. P. Hambleton and S. W. Sloan, “A Perturbation Method for Optimization of Rigid Block Mechanisms in the Kinematic Method of Limit Analysis,” Computers and Geotechnics, Vol. 48, 2013, pp. 260-271.

http://dx.doi.org/10.1016/j.compgeo.2012.07.012

[21] M. Bastani and D. K. Salkuyeh, “A Highly Accurate Method to Solve Fisher’s Equation,” Indian Academy of Sciences, Vol. 78, No. 3, 2012, pp. 335-346.

[22] W. Y. Yang, W. Cao, T. Chung, J. Morris, et al., “Applied Numerical Methods Using Matlab,” John Wiley & Sons, Hoboken, New Jersey, 2005. http://dx.doi.org/10.1002/0471705195

[23] E. Kreyszig, “Advanced Engineering Mathematics,” John Wiley & Sons, Columbus, 2006.