In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM...In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.展开更多
In this paper, the existence and uniqueness of solution of singular Hammerstein-Volterra integral equation (<strong>H-VIE</strong>) are considered. Toeplitz matrix (<strong>TMM</strong>) and pr...In this paper, the existence and uniqueness of solution of singular Hammerstein-Volterra integral equation (<strong>H-VIE</strong>) are considered. Toeplitz matrix (<strong>TMM</strong>) and product Nystrom method (<strong>PNM</strong>) to solve the <strong>H-VIE</strong> with singular logarithmic kernel are used. The absolute error is calculated.展开更多
We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions.We employ the standard semi-implicit numerical scheme,which treats the linear fourth-order dissipatio...We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions.We employ the standard semi-implicit numerical scheme,which treats the linear fourth-order dissipation term implicitly and the nonlinear term explicitly.Under natural constraints on the time step we prove strict phase separation and energy stability of the semiimplicit scheme.This appears to be the first rigorous result for the semi-implicit discretization of the Cahn-Hilliard equation with singular potentials.展开更多
In this paper, we obtain the（W Hω^1, W Lω^1） type estimate for the Marcinkiewicz integral and the（W H1 b,ω, W L1ω） type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, w...In this paper, we obtain the（W Hω^1, W Lω^1） type estimate for the Marcinkiewicz integral and the（W H1 b,ω, W L1ω） type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition.展开更多
文摘In the paper, the approximate solution for the two-dimensional linear and nonlinear Volterra-Fredholm integral equation (V-FIE) with singular kernel by utilizing the combined Laplace-Adomian decomposition method (LADM) was studied. This technique is a convergent series from easily computable components. Four examples are exhibited, when the kernel takes Carleman and logarithmic forms. Numerical results uncover that the method is efficient and high accurate.
文摘In this paper, the existence and uniqueness of solution of singular Hammerstein-Volterra integral equation (<strong>H-VIE</strong>) are considered. Toeplitz matrix (<strong>TMM</strong>) and product Nystrom method (<strong>PNM</strong>) to solve the <strong>H-VIE</strong> with singular logarithmic kernel are used. The absolute error is calculated.
基金supported in part by Hong Kong RGC grant GRF Nos.16307317,16309518partially supported by the NSFC grants Nos.11731006,K20911001,NSFC/RGC No.11961160718the Science Challenge Project(No.TZ2018001)。
文摘We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions.We employ the standard semi-implicit numerical scheme,which treats the linear fourth-order dissipation term implicitly and the nonlinear term explicitly.Under natural constraints on the time step we prove strict phase separation and energy stability of the semiimplicit scheme.This appears to be the first rigorous result for the semi-implicit discretization of the Cahn-Hilliard equation with singular potentials.
基金Supported by National Natural Science Foundation of China(Grant Nos.11001266,11171345)Beijing Higher Education Young Elite Teacher Project(Grant No.YETP0946)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)
文摘In this paper, we obtain the（W Hω^1, W Lω^1） type estimate for the Marcinkiewicz integral and the（W H1 b,ω, W L1ω） type estimate for the commutator generated by a BMO function and the Marcinkiewicz integral, where the kernel satisfies a certain logarithmic type Lipschitz condition.
