In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterati More
In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica. In this paper, we consider a generalized form of nonlinear Schrodinger with second-order spatiotemporal dispersion coefficients. The generalized exponential rational function method (GERFM) have been used to obtain some novel exact optical solutions. Also, a new iterative method is successfully examined to numerical solution of the equation. Several numerical simulations are provided to show the behavior of the exact solution, and reveal the efficiently of the numerical results. It is apparent that both employed methods are simple but quite efficient for the extraction of solutions of the problem. Moreover, they are applicable for solving other nonlinear problems arising in mathematics, physics and other branches of engineering. All computations and numerical simulations are carried out with Mathematica.
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Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solv More
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence./////////Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. Stability, consistency, and (therefore) convergence of the method are examined. It is shown that the fractional method based on the shifted Grunwald formula is unconditionally stable. This study concerns both theoretical and numerical aspects, where we deal with the construction and convergence analysis of the discretization schemes. A numerical example is presented and compared with exact solution for its order of convergence.
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The element free Galerkin method is a well-known method for solving partial differential equations. Applying essential boundary conditions in this method, that based on moving least squares approximation, have some complexities. Since the shape functions of the moving l More
The element free Galerkin method is a well-known method for solving partial differential equations. Applying essential boundary conditions in this method, that based on moving least squares approximation, have some complexities. Since the shape functions of the moving least squares approximation do not satisfy the property of Kronecker delta function, therefore imposing essential boundary conditions is not as trivial as in the finite element method and we need some modifications of the Galerkin weak form of the equation. In this paper we propose a new approach to apply essential boundary conditions in element free Galerkin method for solving elliptic PDEs. This approach is based on interpolating moving least square method. First we apply the essential boundary conditions in the moving least square approximation of the function then the approximation is used in element free Galerkin method. Thus the essential boundary condition is applied directly. In this paper we first introduce the interpolating moving least squares approximation, and then describe how to apply the boundary conditions. Finally, some different examples show the accuracy and efficiency of the method.
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