A novel method for solving KdV equation based on reproducing kernel hilbert space method

We propose a reproducing kernel method for solving the KdV equation with initial condition based on the reproducing kernel theory. The exact solution is represented in the form of series in the reproducing kernel Hilbert space. Some numerical examples have also been studied to demonstrate the accuracy of the present method. Results of numerical examples show that the presented method is effective

A comparison on solutions of fifth-order boundary-value problems

A fast and accurate numerical scheme for the solution of fifth-order boundary-value problems has been investigated in this work. We apply the reproducing kernel method (RKM) for solving this problem. The analytical results of the equations have been acquired in terms of convergent series with easily computable components. We compare our results with the numerical methods: B-spline method, decomposition method, variational iteration method, Sinc-Galerkin method and homotopy perturbation method. The comparison of the results with exact ones is made to confirm the validity and efficiency

Generalized squared remainder minimization method for solving multi-term fractional differential equations

In this paper, we introduce a generalization of the squared remainder minimization method for solving multi-term fractional differential equations. We restrict our attention to linear equations. Approximate solutions of these equations are considered in terms of linearly independent functions. We change our problem into a minimization problem. Finally, the Lagrange-multiplier method is used to minimize the resultant problem. The convergence of this approach is discussed and theoretically investigated. Some relevant examples are investigated to illustrate the accuracy of the method, and obtained results are compared with other methods to show the power of applied method

Compactons and topological solitons of the Drinfel'd–Sokolov system

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions

On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He\u27s Homotopy Perturbation Method

In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian\u27s decomposition and homotopy perturbation methods and numerical results are compared with exact solutions

Lie symmetry analysis, exact solutions and conservation laws for the time fractional modified Zakharov–Kuznetsov equation

In this work, Lie symmetry analysis (LSA) for the time fractional modified Zakharov–Kuznetsov (mZK) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional mZK equation to nonlinear ordinary differential equation (ODE) of fractional order using its point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi–Kober (EK) sense. We obtained exact traveling wave solutions by using fractional DξαG/G-expansion method. Using Ibragimov's nonlocal conservation method to time fractional nonlinear partial differential equations (FNPDEs), we compute conservation laws (CLs) for the mZK equation

Enhancement of the Hydrodynamic Characteristics in Shell-and-Tube Heat Exchangers by Using W-Baffle Vortex Generators

Improving the hydrodynamic characteristics of STHECs (Shell-and-Tube Heat Exchanger Channels) by using BVGs (Baffle-type Vortex Generators) is among the common passive methods due to their proved efficiency. In this computational investigation, the same method is used to enhance the hydrodynamic behavior of STHECs, by inserting W-shaped Baffle-type Vortex Generators. The numerical model represented by the computational FVM (Finite Volume Method) is used to simulate and analyzed the considered physical model. The fluid used is air, its thermal physical properties are constant, turbulent, incompressible, and its temperature is 300 K at the inlet section of the STHEC. The flow velocity ( Uin ) and atmospheric pressure ( Patm ) are considered as boundary conditions at the entrance (x = 0) and exit (x = L) of the channel, respectively. The results showed that the friction coefficients were related to the pressure, velocity, and Reynolds number values. High values of Re yielded an acceleration of the fluid, resulting thus in increased pressure on the solid walls and augmented friction values