一种修正的Laplace-同伦摄动算法

在NDLT-HPM(非线性分布Laplace-同伦摄动算法)的基础上，通过引入参数h，提出了一种修正的NDLT-HPM(简称MNDLT-HPM)，参数的引入使得求解更加灵活，且能调节和控制级数解的收敛域，克服了NDLT-HPM在嵌入参数p=1处级数解可能不收敛的局限性，使得级数解可以有效地收敛至精确解，从而获得足够精确的解析近似解，两个数值实例表明了该解法的优越性和精确性.

A Modified Laplace-Homotopy Perturbation Algorithm

A modified NDLT-HPM (MNDLT-HPM for short) was proposed through introduction of a parameter into the NDLT-HPM (nonlinearities distribution Laplace transform-homotopy perturbation method). This parameter makes the solving process for the nonlinear differential equations more flexible and is able to adjust and control the convergence region of the series solution, meanwhile overcomes the limitations of the NDLT-HPM that the series solution may be non-convergent when embedded parameter p equals 1. The present algorithm gives series solutions which converge well to the corresponding exact ones, thus obtaining sufficiently accurate approximate analytical solutions. 2 numerical examples show the advantage and accuracy of this method.