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 Study of Rosenau-KdV Equation Using Finite Element Method Based on Collocation Approach

In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms L2 and L∞ are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves

Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation

In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and a priori error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable

Genelleştirilmiş Rosenau-KdV ve genelleştirilmiş Rosenau-RLW denklemlerinin kollokasyon yöntemi ile nümerik çözümleri

Bu tezde genelleştirilmiş Rosenau-KdV ve genelleştirilmiş Rosenau-RLW denklemlerinin sayısal çözümleri yedinci (septic) dereceden B-spline fonksiyonlar kullanılarak Kollokasyon yöntemi ile elde edilmiştir. Bu tez dört bölümden oluşmaktadır. Tezin birinci bölümünde Sonlu Elemanlar yöntemi, Kollokasyon yöntemi ve B-spline fonksiyonlar hakkında bilgiler sunulmuştur. Tezin ikinci bölümünde geneleştirilmiş Rosenau-KdV denklemi tanıtıldı ve yedinci dereceden B-spline fonksiyonlar kullanılarak Kollokasyon yöntemi ile nümerik çözümleri elde edilmiştir. Tezin üçüncü bölümünde genelleştirilmiş Rosenau-RLW denklemi verilerek yedinci dereceden B-spline fonksiyonlar kullanılarak Kollokasyon yöntemi ile nümerik çözümleri elde edilmiştir. Tezin son bölümünde ise elde ettiğimiz nümerik değerlere ilişkin sonuç ve öneriler sunulmuştur

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

Bazı sığ su dalga denklemlerinin sonlu elemanlar yöntemi ile sayısal çözümleri

Altı bölümden olu¸san bu doktora tez çalı¸smasında, B-spline yaklaşım fonksiyonlarına bağlı sonlu elemanlar yöntemleri kullanılarak bazı sığ su dalga denklemlerinin sayısal çözümleri üzerinde çalışılmıştır. Elde edilen sayısal sonuçlar literatürde yer alan teorik ve diger sayısal sonuçlarla karşılaştırılmıştır