解双抛物型方程的两类恒稳差分格式

Two Classes of Steady Difference Schemes for Solving Biparabolic Equation

提出解双抛物型方程的两类新的具三对角线型系数矩阵的三层隐式差分格式 ,其局部截断误差阶分别为O(τ2 +h2 +τh)及O(τ2 +h2 +(τh) 2 ) .它们都是绝对稳定的且可用追赶法求解 .数值例子表明这些格式是有效的 ,理论分析是正确的 .

For solving biparabolic equation, the author presents two new classes of three layered implicit difference schemes with tridigonal matrix of coefficients. Their local truncation errors are in the order of O(τ 2+h 2+τh) and O(τ 2+h 2+(τh) 2) respectively. They are all absolutely stable and can be solved by speedup method. These schemes are shown by numerical example to be effective.