New iterative method for solving gas dynamic equation
In this paper, the gas dynamic equation is solved through new iterative method (NIM). The obtained results are compared with those of homotopy perturbation method (HPM), variational iteration method with He's polynomials (VIMHP) and Laplace transform new homotopy perturbation method (LTNHPM). It is noted that the NIM in case of nonhomogeneous problems takes the form of a convergent series with easily computable components. This method is able to solve large class of linear and nonlinear equations effectively, more easily and accurately; and thus the method has been widely applicable to solve any class of equations in sciences and engineering.
Keywords: New Iterative Method, Homotopy Perturbation Method, Variational Iteration Method with He's Polynomials, Laplace Transform New Homotopy Perturbation Method, Gas Dynamic Equation.
Rathakrishnan, E., Gas Dynamics. Prentice Hall of India Pvt. Ltd. ISBN, 2006.
V. D. Gejji, S. Bhalekar, Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method, Computers & Mathematics with Applications. 59 (2010) 1801-1809.
A. Bibi, A. Kamran, U. Hayat, S. Mohyud-Din, new iterative method for time fractional schrodinger equations, World Journal of Modelling and Simulation. 9 (2013) 89-95.
S. Bhalekar, V. D. Gejji, New iterative method: application to partial differential equations, Applied Mathematics and Computation. 203 (2008) 778-783.
A. A. Hemeda, New iterative method: an application for solving fractional physical differential equations, Journal of Abstract and Applied Analysis. Vol. 2013, Article ID 617010, 9 pages, 2013.
M. A. Ramadan, M. S. Al-Luhaibi, New Iterative Method for Solving the Fornberg-Whitham Equation and Comparison with Homotopy Perturbation Transform Method, British Journal of Mathematics & Computer Science, 4 (2014) 1213-1227.
V. D. Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, Journal of Mathematical Analysis and Applications. 316 (2006) 753-763.
G. Adomian, Solving Frontier problems of physics. The Decomposition Method, Kluwer, Boston, 1994.
J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering. 178 (1999) 257-262.
J.H. He, Variational iteration method-akind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics. 34 (1999) 699-708.
Y. Cherruault, Convergence of Adomian’s method, Kybernetes, 18 (1989) 31-38.
A. J. Jerri, Introduction to Integral Equations with Applications, Wiley-Interscience, New York, NY, USA, 2nd edition, 1999.
S. Bhalekar, V. D. Gejji, Convergence of the New Iterative Method, International Journal of Differential Equations. 2011, Article ID 989065, 10 pages.
H. Jafari, M. Zabihi, M. saidy, Application of homotopy perturbation method for solving gas dynamic equation, Applied Mathematical Sciences, 2 (2008) 2393- 2396.
Hossein Aminikhah and Ali Jamalian, Numerical approximation for nonlinear gas dynamic equation, International Journal of Partial Differential Equations, Vol. 2013, Article ID 846749, 7 pages, 2013.
M. matinfar, M. saeidy, M. mahdavi and M. rezael, The variational iteration method for exact solution of gas dynamic equation using He's polynomials, Bulletin of Mathematical Analysis and Applications, 3 (2011) 50-55.