全离散配置法求解一类拟线性抛物方程

A discrete-time collocation method for a class of quasilinear parabolic equations

讨论一类拟线性抛物方程的初边值问题 ,提出了有限配置与有限差分相结合的全离散配置格式 ,证明了时间步长充分小的条件下全离散解的存在唯一性 ,并分析得到最优阶的H1

It is formulated that a discrete-time collocation scheme which combines collocation and finite difference for solving a class of quasilinear parabolic equations on a rectangle with the solution subject to homogeneous boundary condition. It is showed that for sufficiently small time stepsize the solution to the scheme is unique and of optimal-order accuracy in space in the H 1 norm.