论文标题
非线性自主和非自主波形方程的快速收敛近似方案
A rapidly convergent approximation scheme for nonlinear autonomous and non-autonomous wave-like equations
论文作者
论文摘要
在这项工作中，已经提出了一种有效的近似方案，以获得具有恒定或可变系数的非线性偏微分方程的准确近似解，该方程在一系列指数中而不是自变量的代数函数中满足初始条件。结果：i）该系列的收敛速度比其他几种方法和ii）得出的速度快，而ii）确切的分析解决方案可以从近似解决方案系列的前几个术语中获得，如果方程是可以整合的。已经建立了连续校正项之和的收敛性，并且还提出了近似值中误差的估计。本方法的效率已通过一些方程中存在各种非线性术语的示例来说明。
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.
