摘要
本文讨论下述定解问题的差分解法 u_t(x,t)=Au_(xx)(x,t)+f(u),(x,t)∈Q_T=(0,L)×(0,T) u_x(0,t)—σ_1u(0,t)=0,σ_1>0,t∈[0,T]; u_x(L,t)+σ_2u(L,t)=0,σ_2>0,t∈[0,T]; u(x,0)=■(x),x∈[0,L].其中u(x,t)=(u_1(x,t),…,u_m(x,t)),f(u)=f(f_1(u),…,f_m(u)),■(x)=(■_1(x),…■_m(x))满足适定性条件。
The purpose of this paper consists in showing the existence and, uniqueness of the generalized global solution and approxilnate solution of the third boundary problenm for the systems of generalized Schrodinger type. The author of [1] has solved the first and second boundary problems for the same systems. In this paper,we solved the third boundary problem by the method of [1]. We have constructed the finite difference scheme and proved the existence and uniqueness of the solu-tion of fhe finite difference scheme. Finally we have proved that the solution of the
finite difference scheme converges to the unique generalized global solution of the original problem.
出处
《应用数学与计算数学学报》
1989年第1期92-94,共3页
Communication on Applied Mathematics and Computation
