Blowing-up solutions of the time-fractional dispersive equations

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.Comment: 24 page

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes.info:eu-repo/semantics/publishedVersio

Numerical Analysis of a Linear-Implicit Average Scheme for Generalized Benjamin-Bona-Mahony-Burgers Equation

A linear-implicit finite difference scheme is given for the initial-boundary problem of GBBMBurgers equation, which is convergent and unconditionally stable. The unique solvability of numerical solutions is shown. A priori estimate and second-order convergence of the finite difference approximate solution are discussed using energy method. Numerical results demonstrate that the scheme is efficient and accurate

Solitary-wave solutions of the GRLW equation using septic B-spline collocation method

In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different lin- earization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L 2 and L ∞ and the invari- ants I 1 , I 2 and I 3 . A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numer- ical scheme is preferable to some recent numerical schemes

GEW ve GRLW denklemlerinin sonlu elemanlar yöntemi ile sayisal çözümleri

Bu tez c¸alıs¸masında, GEW ve GRLW denklemleri, B-spline fonksiyonlar kullanılarak kollokasyon ve Galerkin sonlu elemanlar yontemleri ile sayısal olarak çozüldü. Von-Neumann tekniği kullanılarak, lineerleştirilmis¸ algoritmaların şartsız kararlı olduğu g österildi. Sayısal algoritmalar; tek solitary dalga, iki ve üç¸ solitary dalganın etkileşimi, Maxwellian başlangıç şartı ile dalga oluşumu ve ardışık dalgaların gelişimini içeren orneklere uygulanarak test edildi. Sayısal algoritmaların performansını kanıtlamak için, L2 ve L∞ hata normları hesaplandı ve daha önce elde edilen sayısal sonuçlarla karşılaştırıldı. Sayısal algoritmaların kütle, momentum ve enerji ile ilgili ozellikleri koruduğunu göstermek için I1, I2 ve I3 ile ifade edilen korunum sabitlerindeki degişim hesaplandı. Ayrıca, solitary dalgaların farklı zamanlardaki hareketleri grafik çizilerek gosterildi

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools