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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The regularity with respect to domains of the additive eigenvalues of super-quadratic Hamilton-Jacobi equation
超二次 哈密尔顿-雅可比方程 加性特征值域 规律性
2023/4/27
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
We show that any global convex solution to the Sigma-2 equation must be quadratic.
Numerical Solution of Generalized Abel’s Integral Equation by Variational Iteration Method
Variational Iteration Method Singular Integral Equation Abel’s Kernel
2013/1/30
In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approxi...
Effective Solution of Riemann Problem for Fifth Order Improperly Elliptic Equation on a Rectangle
polyharmonic Equation Boundary Value Problem Dirichlet Problem Improperly Elliptic Equation Riemann Problem Grid Method
2013/1/30
In this paper we present a numerical method for solving Riemann type problem for the fifth order improperly elliptic equation in complex plane .We reduce this problem to the boundary value problems fo...
The Best Finite-Difference Scheme for the Helmholtz Equation
The Best Finite-Difference Scheme for the Helmholtz and Laplace’s Equations
2013/1/30
The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on seve...
A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation
Schrodinger Equation Absorbing Boundary FDTD Method Stability
2013/1/30
The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schr?dinger equation in an iterative process. However, the method...
New type of KP equation with self-consistent sources and its bilinear B鋍klund transformation
New type of KP equation self-consistent
2012/8/8
A new type of the KP equation with self-consistent sources (KPESCS)
痳st found by Melnikov ( Lett. Math. Phys. 7(1983) 129-136)is re-constructed
via source generation procedure. New feature of the ob...
Conservativity of Symplectic Methods for the Ablowitz-Ladik Discrete Nonlinear Schrodinger Equation
Nonlinear Schrdinger Equation Ablowitz-Ladik Model Darboux
2012/8/7
Using several kinds of Darboux transformations, we standardize the non-
canonical symplectic structure of Ablowitz-Ladik model (A-L model) of the
Nonlinear Schr膐dinger Equation (NLSE), then we emplo...
Numerical Solution of the Fredholme-Volterra Integral Equation by the Sinc Function
Fredholme-Volterra Integral Equation Sinc Function Collocation Method
2013/1/30
In this paper, we use the Sinc Function to solve the Fredholme-Volterra Integral Equations. By using collocation method we estimate a solution for Fredholme-Volterra Integral Equations. Finally conver...
A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation
integro-differential equation continuous Galerkin finite element method convolution kernel stability a posteriori estimate
2012/5/9
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error repres...
Convergence analysis of a multigrid algorithm for the acoustic single layer equation
Convergence analysis multigrid algorithm acoustic single layer equation
2012/2/29
We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions an...
An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation
Poisson’s Equation Finite Difference Method Tri-diagonal Matrix Hockney’s Method Thomas Algorithm
2013/1/30
In this work, the three dimensional Poisson’s equation in Cartesian coordinates with the Dirichlet’s boundary conditions in a cube is solved directly, by extending the method of Hockney. The Poisson e...
Solution of the Generalized Abel Integral Equation by Using Almost Bernstein Operational Matrix
Abel Inversion Bernstein Polynomials Almost Bernstein Operational Matrix Of Integration Noise Resistance
2013/1/30
A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier pr...
General Solution of Generalized (2+1)–Dimensional Kadomtsev-Petviashvili (KP) Equation by Using the –Expansion Method
(G,/G)-Expansion Method Generalized Kadomtsev-Petviashvili (KP) Equation Hyperbolic Function Solutions Trigonometric Function Solutions
2013/1/30
In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our w...
A Fourth Order Improved Numerical Scheme for the Generalized Burgers—Huxley Equation
Burgers-Huxley Finite-Difference Method Modified Predictor-Corrector
2013/1/30
A fourth order finite-difference scheme in a two-time level recurrence relation is proposed for the numerical solution of the generalized Burgers--Huxley equation. The resulting nonlinear system, whic...