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Hypercomplex mathematics and HPM for the time-delayed Burgers equation with convergence analysis. (English) Zbl 1227.65098
The authors discuss hypercomplex mathematics and the homotopy perturbation method (HPM) for the time delayed Burgers equation with convergence analysis. Convergence conditions are discussed. The obtained numerical solutions using the HPM are presented. The Banach fixed point theory is used in their discussion.
##### MSC:
 65M70 Spectral, collocation and related methods (IVP of PDE) 35Q53 KdV-like (Korteweg-de Vries) equations 65M12 Stability and convergence of numerical methods (IVP of PDE)
##### References:
 [1] Ahmed, E., Abusalam, H.A.: On modified Black–Scholes equation. Chaos, Solitons Fractals 23, 42–52 (2004) [2] Atkinson, K., Han, W.: Theoritical Numerical Analysis. Springer, New York (2009) [3] Chun, C., Sakthivel, R.: Homotopy perturbation technique for solving two-point boundary value problems-comparison with other methods. Comput. Phys. Commun. 181, 1021–1024 (2010) · Zbl 1216.65094 · doi:10.1016/j.cpc.2010.02.007 [4] Davenport, M.: Commutative Hypercomplex Mathematics. Comcast.net/$\sim$cmdaven/burgers.htm (2008) [5] Davenport, M.: The General Analytical Solution for the Burgers Equation. Comcast.net/$\sim$cmdaven/burgers.htm (2008) [6] Dugard, L., Verriest, E.I.: Stability and control of time-delay systems. In: Lecture Notes in Control and Information Sciences, vol. 228. Springer (1997) [7] Fahmy, E.S., Abdusalam, H.A., Raslan, K.R.: On the solutions of the time-delayed Burgers equation. Nonlinear Anal. 69, 4775–4786 (2008) · Zbl 1165.35304 · doi:10.1016/j.na.2007.11.027 [8] Kar, S., Banik, S.K., Ray, D.S.: Exact solutions of Fisher and Burgers equations with finite transport memory. J. Phys. A 24, 77–83 (2003) [9] Kim, H., Sakthivel, R.: Travelling wave solutions for time-delayed nonlinear evolution equations. Appl. Math. Lett. 23, 527–532 (2010) · Zbl 1189.35281 · doi:10.1016/j.aml.2010.01.005 [10] Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Inc., New York (1993) [11] Okubo A.: Diffusion and Ecological Problems: Mathematical Models Biomathematics 10. Springer-Verlag, Berlin, Heidelberg et New York, XIII (1980) [12] Saadatmandi, A., Dehghan, M., Eftekhari, A.: Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems. Nonlinear Anal.: Real World Appl. 10, 1912–1922 (2009) · Zbl 1162.34307 · doi:10.1016/j.nonrwa.2008.02.032 [13] Sakthivel, R., Chun, C., Areum Bae, A.: A general approach to hyperbolic partial differential equations by homotopy perturbation method. Int. J. Comput. Math. 87, 2601–2606 (2010) · Zbl 1203.35060 · doi:10.1080/00207160802691660 [14] Shakeri, F., Dehghan, M.: Solution of delay differential equations via a homotopy perturbation method. Math. Comput. Model. 48(3–4), 486–498 (2008) · Zbl 1145.34353 · doi:10.1016/j.mcm.2007.09.016 [15] Shakeri, F., Dehghan, M.: Solution of delay differential equations via a homotopy perturbation method. Math. Comput. Model. 48, 486–498 (2008) · Zbl 1145.34353 · doi:10.1016/j.mcm.2007.09.016 [16] Vendhan, C.P.: A study of Berger equations applied to nonlinear vibrations of elastic plates. Int. J. Mech. Sci. 17, 461–468 (1975) · doi:10.1016/0020-7403(75)90045-4