内蒙古师范大学学报(自然科学汉文版)
內矇古師範大學學報(自然科學漢文版)
내몽고사범대학학보(자연과학한문판)
Journal of Inner Mongolia Normal University (Natural Science Edition)
2015年
5期
574-580
,共7页
偏微分方程%同伦摄动%非线性%解析解
偏微分方程%同倫攝動%非線性%解析解
편미분방정%동륜섭동%비선성%해석해
partial differential equation%homotopy perturbation%nonlinear%analytic solution
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。
對一種新的同倫攝動方法進行瞭推廣,使其能夠對更一般形式的偏微分方程進行求解。利用推廣的同倫攝動法對線性非齊次微分方程、3+1維四階橢圓微分方程、彊非線性微分方程和含有混閤偏導數項的微分方程進行求解,均得到瞭解析解且收斂到精確解,驗證瞭該方法求解非線性偏微分方程的有效性。
대일충신적동륜섭동방법진행료추엄,사기능구대경일반형식적편미분방정진행구해。이용추엄적동륜섭동법대선성비제차미분방정、3+1유사계타원미분방정、강비선성미분방정화함유혼합편도수항적미분방정진행구해,균득도료해석해차수렴도정학해,험증료해방법구해비선성편미분방정적유효성。
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.