We construct and analyze a family of semi-discretized difference schemes with two parameters for the Korteweg-de Vries (KdV) equation. The scheme possesses the first four near-conserved quantities for periodic boundar...We construct and analyze a family of semi-discretized difference schemes with two parameters for the Korteweg-de Vries (KdV) equation. The scheme possesses the first four near-conserved quantities for periodic boundary conditions. The existence and the convergence of its global solution in Sobolev space L-infinity(0,T;H-3) are proved and the scheme is also stable about initial values. Furthermore, the scheme conserves exactly the first two conserved quantities in the special case.展开更多
Presents a study which proposed a numerical solution of first kind integral equation for the Helmholtz equation on smooth open arcs. Quadrature method used; Numerical examples.
In this paper we investigate the existence, uniqueness and regularity of the solution of semilinear parabolic equations with coefficients that are discontinuous across the interface, some prior estimates are obtained....In this paper we investigate the existence, uniqueness and regularity of the solution of semilinear parabolic equations with coefficients that are discontinuous across the interface, some prior estimates are obtained. A net shape of the finite elements around the singular points was designed in [7] to solve the linear elliptic problems, by means of that net, we prove that the approximate solution has the same convergence rate as that without singularity.展开更多
文摘We construct and analyze a family of semi-discretized difference schemes with two parameters for the Korteweg-de Vries (KdV) equation. The scheme possesses the first four near-conserved quantities for periodic boundary conditions. The existence and the convergence of its global solution in Sobolev space L-infinity(0,T;H-3) are proved and the scheme is also stable about initial values. Furthermore, the scheme conserves exactly the first two conserved quantities in the special case.
基金the National Natural Science Foundation of China 19901004-1.
文摘Presents a study which proposed a numerical solution of first kind integral equation for the Helmholtz equation on smooth open arcs. Quadrature method used; Numerical examples.
文摘In this paper we investigate the existence, uniqueness and regularity of the solution of semilinear parabolic equations with coefficients that are discontinuous across the interface, some prior estimates are obtained. A net shape of the finite elements around the singular points was designed in [7] to solve the linear elliptic problems, by means of that net, we prove that the approximate solution has the same convergence rate as that without singularity.
