Legendre Approximation for Solving Linear HPDEs and Comparison with Taylor and Bernoulli Matrix Methods

Emran Tohidi^{*}

Show more

References

[1] B. Bulbul and M. Sezer, “Taylor Polynomial Solution of Hyperbolic Type Partial Differential Equations with Constant Coefficients,” International Journal of Computer Mathematics, Vol. 88, No. 3, 2011, pp. 533-544.
doi:10.1080/00207161003611242

[2] E. Tohidi, and M. Shirazian, “Numerical Solution of Linear HPDEs via Bernoulli Operational Matrix of Differentiation and Comparison with Taylor Matrix Method,” Mathematical Science Letters, Accepted.

[3] M. Dehghan and A. Shokri, “A Numerical Method for Solving the Hyperbolic Telegraph Equation,” Numerical Methods for Partial Differential Equations, Vol. 24, No. 4, 2008, pp. 1080-1093. doi:10.1002/num.20306

[4] A. Ashyralyev and M. E. Koksal, “On the Numerical Solution of Hyperbolic PDE with Variable Space Operator,” Numerical Methods for Partial Differential Equations, Vol. 25, No. 5, 2009, pp. 1086-1099.
doi:10.1002/num.20388

[5] F. Gao and C. Chi, “Unconditionally Stable Difference Schemes for a One-Space-Dimensional Linear Hyperbolic Equation,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 1272-1276.
doi:10.1016/j.amc.2006.09.057

[6] R. K. Mohanty and M. K. Jain, “An Unconditionally Stable Alternating Direction Implicit Scheme for the Two Space Dimensional Linear Hyperbolic Equation,” Numerical Methods for Partial Differential Equations, Vol. 17, No. 6, 2001, pp. 684-688. doi:10.1002/num.1034

[7] R. K. Mohanty, M. K. Jain and U. Arora, “An Unconditionally Stable Adi Method for the Linear Hyperbolic Equation in Three Space Dimensions,” International Journal of Computer Mathematics, Vol. 79, No. 1, 2002, pp. 133-142. doi:10.1080/00207160211918

[8] R. K. Pandy, N. Kumar, A. Bhardwaj and G. Dutta, “Solution of Lane-Emden Type Equations Using Legendreoperational Matrix of Differentiation,” Applied Mathematics and Computation, Vol. 218, No. 14, pp. 76297637.

[9] J. Biazar and H. Ebrahimi, “An Approximation to the Solution of Hyperbolic Equations by Adomian Decomposition Method and Comparison with Characteristics Method,” Applied Mathematics and Computation, Vol. 163, No. 2, 2005, pp. 633-638.
doi:10.1016/j.amc.2004.04.005

[10] X. Yang, Y. Liu and S. Bai, “A Numerical Solution of Second-Order Linear Partial Differential Equations by Differential Transform,” Applied Mathematics and Computation, Vol. 173, No. 2, 2006, pp. 792-802.
doi:10.1016/j.amc.2005.04.015