In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations...
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In this paper,we investigate the vanishing viscosity limit of the 3D incompressible micropolar equations in bounded domains with boundary *** is shown that there exist global weak solutions of the micropolar equations in a general bounded smooth *** particular,we establish the uniform estimate of the strong solutions for when the boundary is ***,we obtain the rate of convergence of viscosity solutions to the inviscid solutions as the viscosities tend to zero(i.e.,(ε,χ,γ,κ)→0).
In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solv...
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In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the *** particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing ***,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial *** derive optimal order a p...
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In this paper,we study a posteriori error estimates of the L1 scheme for time discretizations of time fractional parabolic differential equations,whose solutions have generally the initial *** derive optimal order a posteriori error estimates,the quadratic reconstruction for the L1 method and the necessary fractional integral reconstruction for the first-step integration are *** using these continuous,piecewise time reconstructions,the upper and lower error bounds depending only on the discretization parameters and the data of the problems are *** numerical experiments for the one-dimensional linear fractional parabolic equations with smooth or nonsmooth exact solution are used to verify and complement our theoretical results,with the convergence ofαorder for the nonsmooth case on a uniform *** recover the optimal convergence order 2-αon a nonuniform mesh,we further develop a time adaptive algorithm by means of barrier function recently *** numerical implementations are performed on nonsmooth case again and verify that the true error and a posteriori error can achieve the optimal convergence order in adaptive mesh.
For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin *** basis functions for the provided method are selected generalize...
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For fractional Volterra integro-differential equations(FVIDEs)with weakly singular kernels,this paper proposes a generalized Jacobi spectral Galerkin *** basis functions for the provided method are selected generalized Jacobi functions(GJFs),which can be utilized as natural basis functions of spectral methods for weakly singular FVIDEs when appropriately *** developed method's spectral rate of convergence is determined using the L^(∞)-norm and the weighted L^(2)-*** results indicate the usefulness of the proposed method.
In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a phys...
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In view of the fact that impulsive differential equations have the discreteness due to the impulse phenomenon, this article proposes a single hidden layer neural networkmethod-based extreme learning machine and a physics-informed neural network method combined with learning rate attenuation strategy to solve linear impulsive differential equations and nonlinear impulsive differential equations, respectively. For the linear impulsive differential equations, first, the interval is segmented according to the impulse points, and a single hidden layer neural network model is constructed, the weight parameters of the hidden layer are randomly set, the optimal output parameters, and solution of the first segment are obtained by the extreme learning machine algorithm, then we calculate the initial value of the second segment according to the jumping equation and the remaining segments are solved in turn in the same way. Although the single hidden layer neural network method proposed can solve linear equations with high accuracy, it is not suitable for solving nonlinear equations. Therefore, we propose the physics-informed neural network combined with a learning rate attenuation strategy to solve the nonlinear impulsive differential equations, then the Adam algorithm and L-BFGS algorithm are combined to find the optimal approximate solution of each segment. Numerical examples show that the single hidden layer neural network method with Legendre polynomials as the activation function and the physics-informed neural network method combined with learning rate attenuation strategy can solve linear and nonlinear impulsive differential equations with higher accuracy. Impact Statement-It is difficult to obtain the analytical solutions of impulsive differential equations because of the existence of impulse points, and the current numerical methods are complicated and demanding. In recent years, artificial neural network methods have been widely used due to its simplicity and efficie
*** 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.
Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are *** approaches are on account of two-grid skill include two major phases:find the ...
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Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are *** approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency *** error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are *** numerical examples are implemented to verify the algorithm.
This article introduces a kind of stochastic SEIR models containing virus mutation and logistic growth of susceptible populations, whose deterministic versions have a positively invariant set and globally asymptotical...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the othe...
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In this paper,we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's *** propose two a posteriori error estimators,one is the recovery-type estimator,and the other is the residual-type *** first propose the curl-recovery method for the staggered discontinuous Galerkin method(SDGM),and based on the super-convergence result of the postprocessed solution,an asymptotically exact error estimator is *** residual-type a posteriori error estimator is also proposed,and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's *** efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.
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