非齐次热传导方程的高精度隐式格式

IMPLICIT FINTE DIFFERENCE SCHEMES WITH HIGH ORDER ACCURACY FOR INHOMGONEOUS HEAT CONDUCTION EQUATION

采用待定系数和差分逼近方程的最高相容条件相结合的方法，提出了两种精度依次为Ｏ（Ｋ３＋Ｋｈ２＋ｈ２）和Ｏ（Ｋ２＋Ｋｈ２＋ｈ４）的数值求解非齐次热传导方程的两层三点隐式差分格式．所得格式均是无条件稳定的。

Two new two level implicit finite difference methods with absolute stability are developed for inhomogeneous heat conduction equation in this paper. The methods are of order O(K 2+Kh 2+h 2)and O (K 2+Kh 2+h 4) recpectively. Numerical example is given to illustreat the behavior of the present method.