非线性自治和非自治波动方程的快速收敛逼近格式
A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations
摘要：
本文对满足初始条件的常系数或变系数非线性偏微分方程，用指数函数代替自变量的代数函数，给出了一种有效的近似格式，使其能得到精确的近似解.结果是：i）发现级数的收敛速度比用其它方法得到的级数的收敛速度快; ii）在方程可积的情况下，可以从近似解的级数的前几项得到精确分析解。已建立的逐次校正项的和的收敛性，并在近似的误差估计也已提交。本文方法的有效性已通过一些例子与各种非线性项中存在的方程说明。
英文摘要：
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of exponential instead of an algebraic function of independent variables. As a consequence: i) the convergence of the series found to be faster than the same obtained by few other methods and ii) the exact analytic solution can be obtained from the first few terms of the series of the approximate solution, in cases the equation is integrable. The convergence of the sum of the successive correction terms has been established and an estimate of the error in the approximation has also been presented. The efficiency of the present method has been illustrated through some examples with a variety of nonlinear terms present in the equation.
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