Approximate analytical solutions of systems of PDEs by homotopy analysis method

AbstractIn this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions

Construction of (n+ 1) -dimensional dual-mode nonlinear equations: multiple shock wave solutions for (3 + 1) -dimensional dual-mode Gardner-type and KdV-type

The goal of this study is to offer an exclusive functional conversion to produce (n+ 1) -dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3 + 1) -dimensional dual-mode Gradner-type and KdV-type have been established. Finally, the simplified bilinear method is used to tell the necessary conditions on these new models to have multiple singular-solitons. - 2019, The Author(s).This work is financially supported by UKM Grant: DIP-2017-011 and Ministry of Education Malaysia Grant FRGS/1/2017/STG06/UKM/01/1.Scopu

Spectral and distributional problems for homogeneous extensions of dynamical systems and the rate of mixing of two-dimensional Markov shifts

SIGLEAvailable from British Library Document Supply Centre- DSC:DX175859 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A step variational iteration method for solving non-chaotic and chaotic systems

In this paper, a new reliable method called the step variational iteration method (SVIM) based on an adaptation of the variational iteration method (VIM) is presented to solve non–chaotic and chaotic systems. The SVIM uses the general Lagrange multipliers for constructing the correction functional for the problems. The SVIM yields a step analytical solution of the form of a rapidly convergent infinite power series with easily computable terms and obtain a good approximate solution for larger intervals. The accuracy of the presented solution obtained is in an excellent agreement with the previously published solutions

Application of the G′G-expansion method for the generalized Fisher’s equation and modified equal width equation

In this work, the exact traveling wave solutions of the generalized Fisher’s equation and modified equal width equation are studied by using the G′G-expansion method. As a result, many solitary wave solutions are derived from the solutions via hyperbolic functions, trigonometric functions and rational functions. When the parameters were taken at special values, the results obtained were compared with the solution via the tanh method established earlier. In fact, many general non-traveling wave solutions are obtained. The efficiency of the method is demonstrated by applying it for a variety of selected equations

Generalized semi-extremally disconnectedness in double fuzzy topological spaces

In this paper we introduce the concepts of (r, s)-generalized fuzzy semi-extremally disconnectedness spaces and study the effect of generalized double fuzzy semi-irresolute and generalized double fuzzy semiopen functions in this space. Moreover, we investigate some interesting relationship between generalized double fuzzy semiopen functions and (r, s)-generalized fuzzy semi-extremally disconnectedness spaces

New exact solutions of sixth-order thin-film equation

TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values

On e-I-open sets, e-I-continuous functions and decomposition of continuity

In this paper, we introduce the notations of $e-\mathcal{I}$-open sets and strong $\mathcal{B}_{I}^{\star}$ -set to obtain a decomposition of continuing via idealization. Additionally, we investigate properties of $e-\mathcal{I}$-open sets and strong $\mathcal{B}_{I}^{\star}$ -set. Also we studied some more properties of $e-\mathcal{I}$-open sets and obtained several characterizations of $e-\mathcal{I}$-continuous functions and investigate their relationship with other types of functions

New Fixed Point Results for Modified Contractions and Applications

In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming. © 2019 by the authors