中文摘要：

对一种新的同伦摄动方法进行了推广,使其能够对更一般形式的偏微分方程进行求解.利用推广的同伦摄动法对线性非齐次微分方程、3＋1维四阶椭圆微分方程、强非线性微分方程和含有混合偏导数项的微分方程进行求解,均得到了解析解且收敛到精确解,验证了该方法求解非线性偏微分方程的有效性.

英文摘要：

In this paper,the new homotopy perturbation method （NHPM）is used to solve more gener-alized linear and nonlinear differential equation.The analytic solutions of one linear inhomogeneous differ-ential equation,one 3＋1 dimension Fourth-order parabolic differential equation,one nonlinear equation and one differential equation including mixed partial derivative term are obtained by the method.The effective-ness of the method is supported by the fact that all the analytic solutions converge to the exact solutions.