Abstract
Abstract
In this paper, we have constructed two dimensional (2D ) hyperbolic quasi-linear partial differential equations (HQLPDE) by considering two cases. The Cauchy data is given in the form of exponential curve in the 1st case. The initial value problems (IVP) are mentioned as sin x in the 2nd case where as all the cases are associated with time. We have obtained the solutions by using variational iteration method (VIM). In the both cases, we found that solution represents flat surface during the initial stage. We have observed exponential surface in the 1st case and the curved surface in the 2nd case subject to the increasing values of x and y.
Mathematics subject classification: 35Lxx, 35L04
Publisher
Research Square Platform LLC
Reference20 articles.
1. R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Springer-Verlag, New York, 1976. Reprinting of the 1948 original; Applied Mathematical Sciences, Vol. 21. MR0421279 (54 #9284)
2. J. H. He, Comput. Methods Appl. Mech. Eng. 167, 69,(1998).
3. A. M. Wazwaz, J. Comput. Appl. Math. 207, 129(2007).
4. The nonexistence of spurious solutions to discrete, two-point boundary value problems;Thompson HB;Appl. Math. Lett.,2003
5. Variational approach to the sixth-order boundary value problems;He JH;Appl. Math. Comput.,2003