Parabolic Equation Of High Precision And High Stability Format, And Its Parallel Algorithm

In this paper,I design a series of high accuracy serial schemes and parallel algorithms for solving the initial boundary value problem of the parabolic equations by combinatorial difference quotient method and parameters. It has also provided the nimble effective structure method and the new mentality for the algorithm's structure.Regarding serial scheme:One of explicit schemes is designed by us.Its local node space width is three and time is also three.It truncation error is O((?)⁴ + h⁶),the stability condition is r≤1/6. When r takes the special value,its truncation error is 0((?)⁴ + h⁸)One group of implicit schemes is also designed by us.which contains parameters. Its local node space width is three and time is also three. its truncation error is O((?)³ + h⁶),and the stability condition is absolute stability. When the parameter takes the special definite value, its truncation error is O((?)⁴ + h⁸), the stability condition of which is 0 < r < 1/(20)^1/2. when r takes the special definite value, its truncation error is O((?)⁵ + h¹⁰)Regarding parallel algorithm:Firstly, A semi-explicit differencing scheme of two layers and six points and symmetric scheme are presented by combinatorial difference quotient method in this paper,which have a parameter. Then,using the two schemes,we construct group explicit scheme GE parallel algorithm for solving parabolic equation.This algorithm has parameter ,it goes side by side parallel in space and a step-by-step parallel algorithm on time. The truncation error of this algorithm is O((?) +h²) and stability condition.When the parameter takes the special value, its truncation error is O((?)² + h³). When the parameter takes zero and r takes the special value, its truncation error is O((?)² + h⁴).When the points of the space is odd, we set up GEL and GER scheme.Secondly, It has given a kind of new space-time parallel algorithm. This algorithm can be parallel not only on the space,but also can advance together on the time. It has improved algorithm concurrence degree very much, which has developed the tradition can only goes side by side in space but is a step-by-step parallel algorithm on time. It given some new methods of researching algorithm.