K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法...K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法进行讨论,构造了全离散的Chebyshev有理谱格式,并通过对近似解的一系列先验估计,最后得到了近似解的误差估计.展开更多
In this paper, a Legendre spectral method for numerically solving Cahn-Hilliardequations with Neumann boundary conditions is developed. We establish theirsemi-discrete and fully discrete schemes that inherit the energ...In this paper, a Legendre spectral method for numerically solving Cahn-Hilliardequations with Neumann boundary conditions is developed. We establish theirsemi-discrete and fully discrete schemes that inherit the energy dissipation propertyand mass conservation property from the associated continuous problem. we provethe existence and uniqueness of the numerical solution and derive the optimal errorbounds. we perform some numerical experiments which confirm our results.展开更多
In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectra...In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes areproposed, the convergence and stability for the schemes are proved.展开更多
文摘K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法进行讨论,构造了全离散的Chebyshev有理谱格式,并通过对近似解的一系列先验估计,最后得到了近似解的误差估计.
文摘In this paper, a Legendre spectral method for numerically solving Cahn-Hilliardequations with Neumann boundary conditions is developed. We establish theirsemi-discrete and fully discrete schemes that inherit the energy dissipation propertyand mass conservation property from the associated continuous problem. we provethe existence and uniqueness of the numerical solution and derive the optimal errorbounds. we perform some numerical experiments which confirm our results.
文摘In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes areproposed, the convergence and stability for the schemes are proved.
