Current Issue : April - June Volume : 2021 Issue Number : 2 Articles : 5 Articles
The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order α. Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of nonlinearity. Some of the nonlinear equations arise in fluid dynamics and nonlinear phenomena....
It is challenging to reconstruct a nonlinear dynamical system when sufficient observations are not available. Recent study shows this problem can be solved by paradigm of compressive sensing. In this paper, we study the reconstruction of chaotic systems based on the stochastic gradient matching pursuit (StoGradMP) method. Comparing with the previous method based on convex optimization, the study results show that the StoGradMP method performs much better when the numerical sampling period is small. So the present study enables potential application of the reconstruction method using limited observations in some special situations where limited observations can be acquired in limited time....
For a graph G, an ordered set S ⊆V(G) is called the resolving set of G, if the vector of distances to the vertices in S is distinct for every v ∈ V(G). The minimum cardinality of S is termed as the metric dimension of G. S is called a fault-tolerant resolving set (FTRS) for G, if S\{v} is still the resolving set ∀v ∈ V(G). The minimum cardinality of such a set is the fault-tolerant metric dimension (FTMD) of G. Due to enormous application in science such as mathematics and computer, the notion of the resolving set is being widely studied. In the present article, we focus on determining the FTMD of a generalized wheel graph. Moreover, a formula is developed for FTMD of a wheel and generalized wheels. Recently, some bounds of the FTMD of some of the convex polytopes have been computed, but here we come up with the exact values of the FTMD of two families of convex polytopes denoted as Dk for k ≥ 4 and Qk for k ≥ 6. We prove that these families of convex polytopes have constant FTMD. This brings us to pose a natural open problem about the existence of a polytope having nonconstant FTMD....
Iteration problems such as compound interest calculations have well-specified parameters and aim to derive an exact value. Not all problems offer well-specified parameters, even for well-defined dynamic equations; the linear “weak field approximation” of general relativity is iteratively equivalent to Einstein’s non-linear field equation, but the exact parameters involved in some applications are unknown. This paper develops a theory based on “fuzzy” parameters that must produce exact results. The problem is analyzed and example calculations are produced....
In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non- Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phasemodel and employ the fixed unstructuredmesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkinmethod to handle the solution of level set and its reinitialization equations.Amass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed....
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