Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations

Abstract

In this paper, modified variational iteration algorithm-II is investigated for finding approximate solutions of nonlinear Parabolic equations. Comparisons of the MVIA-II with trigonometric B-spline collocation method, variational iteration method, homotopy perturbation transform method, Adomian decomposition method, and modified variational iteration method are carried out, which show that the proposed algorithm (MVIA-II) is robust one. Some nonlinear Parabolic equations are given to demonstrate the implementation and accuracy of the MVIA-II.

On bounds for topological descriptors of φ-sum graphs

“…Moreover, for α = 2 and α = 3, FGZI becomes first Zagreb index and forgotten topological index. Similarly, for β = 1 and β = − 1 2 , GRI becomes second Zagreb index and classical Randić index respectively, see [26][27][28][29][30][31][32].…”

On the decay of exponential type for the solutions in a dipolar elastic body

“…In this sense, it is enough to list a few studies, such as Mindlin [19], Green and Rivlin [20], or Fried and Gurtin [21], which have a good recognition among researchers. Then the number of approaches of these media with dipolar structure has increased considerably [22][23][24][25][26][27][28][29][30][31][32]. Our study is organized as follows.…”

An approximate solution of a differential inclusion with maximal monotone operator

“…This problem has many applications in optimization and fixed-point theory, and there are many papers that studied the exact and approximate solution (see, e.g. [12][13][14]). Our idea to prove the main result of this paper is to use this problem to find an approximate solution of our principle problem (1).…”