解四阶抛物型方程新的高精度显式差分格式

A New Explicit Difference Scheme of High Accuracy for Solving Four-Order Parabolic Equation

对四阶抛物型方程ut+4ux4=0构造了一个新的三层显式高精度差分格式 ,其稳定性条件和局部截断误差阶分别为r =τ/h4<1 / 8和O(τ2 +h6) ,数值例子表明该格式是有效的 ,理论分析是正确的 .

A new three layer explicit difference scheme is proposed for solving four order parabolic equationut+4ux4=0.The scheme meets the stability condition of r=τ/h^4<18 and shows the order of local truncation error of O(τ~2+h^6).A numberal example shows that the scheme is effective and that the analysis of stability is right.