In this work, analytical solutions are provided to the nonlinear equations arising in thermal and flow-induced vibration in fluid-conveying structures using Galerkin-differential transformation method with cosine aftertreatment technique. From the analysis, it was established that increase of the length and aspect ratio of the fluid-conveying structures result in decrease the nonlinear vibratio...

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...

The various industrial, biological and engineering applications of flow of squeezing flow of fluid between parallel plates have been the impetus for the continued interest and generation renewed interests on the subject. As a part of the renewed interests, this paper presents the study of axisymmetric magnetohydrodynamic squeezing flow of nanofluid in porous media under the influence of slip bo...

‎In this paper we establish a new numerical method for solving a class of stochastic partial differential equations (SPDEs) based on B-splines wavelets‎. ‎The method combines implicit collocation with the multi-scale method‎. Using the multi-scale method‎, ‎SPDEs can be solved on a given subdomain with more accuracy and lower computational cost than the rest of the domain‎. ‎The stability and c...

Triple Graph Grammars (TGGs) are a well-known technique for rule-based specification of bidirectional model transformation. TGG rules build up consistent models simultaneously and are operationalized automatically to forward and backward rules describing single transformation steps in the respective direction. These operational rules, however, are of fixed size and cannot describe transformatio...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

‎This article develops a direct method for solving numerically‎ ‎multi delay-fractional differential and integro-differential equations‎. ‎A Galerkin method based on Legendre polynomials is implemented for solving‎ ‎linear and nonlinear of equations‎. ‎The main characteristic behind this approach is that it reduces such problems to those of‎ ‎solving a system of algebraic equations‎. ‎A conver...

In this paper, free convection flow and heat transfer of nanofluids of differently-shaped nano-sized particles over a vertical plate at very low and high Prandtl numbers are analyzed.  The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. T...

The damped Kawahara equation (KE) is nonintegrable and does not have analytical integration. In this work, the powerful numerical method, which reduce differential transformation method (RDTM), devoted to solve KE. accuracy of proved. results are compared with different methods. solution axi-symmetric wave shows effect damping term successfully. We confirmed that RDTM useful for solving equatio...