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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This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tu...
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This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl's mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.
In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak ***,the solution int...
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In this paper,we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak ***,the solution interval is divided into multiple subintervals by weak discontinuity ***,Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each ***,the parameters of the neural network are obtained by training with the extreme learning *** numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.
We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with *** is well known that such equations can be efficiently solved via the structure-preserving doubling algorith...
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We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with *** is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley *** this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special ***,the doubling algorithm based on the proposed generalized transformation is presented and shown to be ***,the convergence result and the comparison theorem on convergent rate are *** numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.
This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time m...
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This paper is concerned with the stability analysis of the exact and numerical solutions of the reaction-diffusion equations with distributed delays. This kind of partial integro-differential equations contains time memory term and delay parameter in the reaction term. Asymptotic stability and dissipativity of the equations with respect to perturbations of the initial condition are obtained. Moreover, the fully discrete approximation of the equations is given. We prove that the one-leg θ-method preserves stability and dissipativity of the underlying equations. Numerical example verifies the efficiency of the obtained method and the validity of the theoretical results.
In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconformin...
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In this paper,we propose a condition that can guarantee the lower bound property of the discrete eigenvalue produced by the finite element method for the Stokes *** check and prove this condition for four nonconforming methods and one conforming *** they produce eigenvalues which are smaller than their exact counterparts.
The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equa...
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The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin *** estimate the error of the numerical solutions in the sense of the *** linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton *** main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine *** estimation for the two-grid solutions is analyzed in *** is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.
In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth ...
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In this paper,we develop a correction operator for the canonical interpolation operator of the Adini *** use this new correction operator to analyze the discrete eigenvalues of the Adini element method for the fourth order elliptic eigenvalue problem in the three *** prove that the discrete eigenvalues are smaller than the exact ones.
We design and numerically validate a recovery based linear finite element method for solving the biharmonic *** main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formula...
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We design and numerically validate a recovery based linear finite element method for solving the biharmonic *** main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element *** operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty *** explicit matrix expression of the proposed method is also *** examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.
In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial tim...
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In this work,we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction-diffusion equation(2D-DOTSFRDE)with low regularity solution at the initial time.A fast evaluation of the distributedorder time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the *** stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are *** the spatial approximation,the finite element method is *** convergence of the corresponding fully discrete scheme is ***,some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.
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