两种变时间步长的显式差分算法

TWO KINDS OF COMPUTATIONAL METHODS IN EXPLICIT DIFFERENCE SCHEME WITH VARIABLE TIME STEPS

针对一类大气、海洋问题，从算子方程出发，在显式完全平方守恒差分格式的基础上提出两种变时间步长的差分算法，使数值计算更加有效。在人工调节时间步长法中，通过人为控制方程中算子能量变化的办法调整时间步长；在自动调节时间步长法中，通过数值试验自动比较出所构造差分格式稳定性的好坏，将它与泰勒展开法及分解算法进行混合应用，验明了自动调节时间步长法具有综合判断差分格式好坏的功能，并得出一些有意义的结论。

Two kinds of computational methods in variable time steps are put forward, on the basis of explicit and complete square conservative difference scheme. which can make numerical computation more efficiently. The first one is the artificial method in adjusting to the time step, which can be realized by controling the variation of operator energy in equation artificially.The automatic method in adjusting to the time step can give out whether the stability of difference scheme is good or not by numerical tests, and can be proved with the function that can synthetically judge the effect of difference scheme by the combined application with the method of Taylor expansion, and the splitting method. At last, some reasonable conclusions have been drawn out.