65 research outputs found

    Numerical solution of the modified equal width wave equation

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    Numerical solution of the modified equal width wave equation is obtained by using lumped Galerkin method based on cubic B-spline finite element method. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. Accuracy of the proposed method is discussed by computing the numerical conserved laws L2 and L∞ error norms. The numerical results are found in good agreement with exact solution. A linear stability analysis of the scheme is also investigated

    Petrov galerkin method with cubic B splines for solving the MEW equation

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    In the present paper, we introduce a numerical solution algorithm based on a Petrov-Galerkin method in which the element shape functions are cubic B-splines and the weight functions quadratic B-splines . The motion of a single solitarywave and interaction of two solitarywaves are studied. Accuracy and efficiency of the proposed method are discussed by computing the numerical conserved laws and L2 , L¥ error norms. The obtained results show that the present method is a remarkably successful numerical technique for solving the modified equal width wave(MEW) equation. A linear stability analysis of the scheme shows that it is unconditionally stable

    Nonlinear Geometric Models

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    A Powerful Robust Cubic Hermite Collocation Method for the Numerical Calculations and Simulations of the Equal Width Wave Equation

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    In this article, non-linear Equal Width-Wave (EW) equation will be numerically solved . For this aim, the non-linear term in the equation is firstly linearized by Rubin-Graves type approach. After that, to reduce the equation into a solvable discretized linear algebraic equation system which is the essential part of this study, the Crank-Nicolson type approximation and cubic Hermite collocation method are respectively applied to obtain the integration in the temporal and spatial domain directions. To be able to illustrate the validity and accuracy of the proposed method, six test model problems that is single solitary wave, the interaction of two solitary waves, the interaction of three solitary waves, the Maxwellian initial condition, undular bore and finally soliton collision will be taken into consideration and solved. Since only the single solitary wave has an analytical solution among these solitary waves, the error norms Linf and L2 are computed and compared to a few of the previous works available in the literature. Furthermore, the widely used three invariants I1, I2 and I3 of the proposed problems during the simulations are computed and presented. Beside those, the relative changes in those invariants are presented. Also, a comparison of the error norms Linf and L2 and these invariants obviously shows that the proposed scheme produces better and compatible results than most of the previous works using the same parameters. Finally, von Neumann analysis has shown that the present scheme is unconditionally stable.Comment: 25 pages, 9 tables, 6 figure

    An Accurate Numerical Solution for the Modified Equal Width Wave Equation Using the Fourier Pseudo-Spectral Method

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    Abstract In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Finally, a Maxwellian initial condition pulse is then studied. The L2 and L∞ error norms are computed to study the accuracy and the simplicity of the presented method

    Toolpath Smoothing using Clothoids for High Speed CNC Machines

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    As a result of this research, new methods for CNC toolpath smoothing were developed. Utilising these methods can increase the speed, decrease vibrations and improve the cut quality of a CNC machine. In the developed techniques, Euler spirals have been used to smooth the corners
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