2023-02

IEEE- Xplore Digital

Recently, the successive approximation method (SAM) has attracted the attention of many authors due to its simplicity, ease of use, and great results. However, the results obtained by SAM start to diverge when the time interval is increased. To address this issue, this paper develops an improved version of the SAM for solving non-linear Partial Differential Equations (PDEs) numerically. Here, the initial condition of the differential equations has been combined with the SAM to obtain stable and more accurate results. The test that was conduct included the original SAM and the improved one on the system of strongly non-linear PDEs. Experimental results revealed that the proposed technique gives better and more accurate numerical solutions regardless of the time interval used.

2021-12

Science Journal of University of Zakho (القضية : 4) (الحجم : 9)

In this paper, we propose two new techniques for solving system of nonlinear partial differential equations numerically, which we first combine Laplace transformation method into a successive approximation method. Second, we combine Padé [2,2] technique into the first proposed technique. To test the efficiency of our techniques, Jaulent-Miodek system was used, which contains partial differential equations and has strongly nonlinear terms. Experimental results revealed that the first proposed technique gives better results when the interval of t is small in terms of error approximation in tabular and graphical manners. Moreover, the results also demonstrated that the second proposed technique gives better results regardless of the given interval of t in terms of the least square errors.

2020-02

General Letters in Mathematics (القضية : 1) (الحجم : 8)

In this paper, Modified Variational Iteration Method (MVIM) and Homotopy Analysis Method (HAM) are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System the (VCVB) system is able to describe the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth, as an example we took the Boussinesq-Burgers (B-B) system, (B-B) system arise in the study of fluid flow and describing the long-wave propagation of shallow water waves. The solutions of these equations helpful for the coastal and civil engineering’s

2018-09

Science Journal of University of Zakho (القضية : 3) (الحجم : 6)

In this paper, Adomian and Adomian-Padé Technique are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System, and using Adomian-Padé Technique for Debug (Remove) The Gap (Complex Root).