By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov te...
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By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative,the fractional central difference operator to discritize the space Riesz fractional partial derivative,and the classical central difference formula to discretize the advection term,a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion *** stability and the convergence analysis of the numerical method are *** experiments show that the numerical method is effective.
A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further c...
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A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical ***, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.
Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Gal...
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Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.
In this paper, the fractional variational integrators for fractional variational problems depending on indefinite integrals in terms of the Caputo derivative are developed. The corresponding fractional discrete Euler-...
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In this paper, the Crank-Nicolson (CN) difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative is studied. The existence of this difference solution is proved ...
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This paper is concemed with numerical method for a two-dimensional timedependent cubic nonlinear Schr(o)dinger *** approximations are obtained by the Galerkin finite element method in space in conjunction with the bac...
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This paper is concemed with numerical method for a two-dimensional timedependent cubic nonlinear Schr(o)dinger *** approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time,*** prove optimal L2 error estimates for two fully discrete schemes by using elliptic projection ***,a numerical example is provided to verify our theoretical results.
In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The con...
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In this paper, we study the Hermite cubic spline collocation method with two parame- ters for solving a initial value problem （IVP） of nonlinear fractional differential equations with two Caputo derivatives. The convergence and nonlinear stability of the method are established. Some illustrative examples are provided to verify our theoretical results. The numerical results also indicate that the convergence order is min{4 - α, 4 - β}, where 0 〈β〈 αa 〈 1 are two parameters associated with the fractional differential equations.
High quality mesh plays an important role for finite element methods in sciencecomputation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and **...
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High quality mesh plays an important role for finite element methods in sciencecomputation and numerical *** the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and *** from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay *** using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.
*** this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodi...
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*** this paper,we propose,analyze and numerically validate a conservative finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic *** use the standard continuous finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time *** mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta *** examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.
Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth *** with the characteristics of deep-sea sediments,the thermo-hydro-...
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Due to the influence of deep-sea environment,deep-sea sediments are usually heterogeneous,and their moduli of elasticity and density change as depth *** with the characteristics of deep-sea sediments,the thermo-hydro-mechanical coupling dynamic response model of heterogeneous saturated porous sediments can be established to study the influence of elastic modulus,density,frequency,and load amplitude changes on the *** on the Green-Lindsay generalized thermoelasticity theory and Darcy’s law,the thermo-hydro-mechanical coupled dynamic response model and governing equations of heterogeneous deep-sea sediments with nonlinear elastic modulus and density are *** analytical solutions of dimensionless vertical displacement,vertical stress,excess pore water pressure,and temperature are obtained by means of normal modal analysis,which are depicted *** results show that the changes of elastic modulus and density have few effects on vertical displacement,vertical stress,and temperature,but have great effects on excess pore water *** the mining machine vibrates,the heterogeneity of deep-sea sediments has great influence on vertical displacement,vertical stress,and excess pore water pressure,but has few effects on *** addition,the vertical displacement,vertical stress,and excess pore water pressure of heterogeneous deep-sea sediments change more *** variation trends of physical quantities for heterogeneous and homogeneous deep-sea sediments with frequency and load amplitude are basically the *** results can provide theoretical guidance for deep-sea mining engineering construction.
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