首先求出了局部区域的近似解析解。
Firstly, the approximate analytical solution of a local domain is derived.
通过扰动方法求得问题的近似解析解。
The approximate analytical solution is got by using perturbation method.
然后采用变量替换，可获得物理平面上的近似解析解。
Then with the use of the substitution of variables. the approximately analytical solution in physical plane can be obtained.
在一些简化假设的基础上，找到了液滴质量燃速的近似解析解。
The approximate analytical solution on the burning rate of droplet mass is also found on the basis of some simplified hyPotheses.
二阶近似解析解和数值解的误差比一阶近似解析解和数值解的误差小。
The error between the numerical solution and the two-order approximate analytic solution is smaller than the error between the numerical solution and the one-order approximate analytic solution.
同时用电子运动模拟计算进行了校验，指出近似解析解有较好的准确性。
The solutions are verified by numerical simulation, showing that the approximate solutions are fairly accurate.
具有一定精度的近似解析解有助于方便分析船舶非线性横摇运动及其稳定性。
An approximate analytical solution with comparative accuracy is helpful in investigating nonlinear rolling of ships and its stability.
同时，指出了近似解析解的局限性，揭示了膜材料的泊松比对结果有较大影响。
At the same time, the limitation of the approximate analytic solution is pointed out because the Poisson ratio of the film materials has strong effect on the results.
当地水文地质条件复杂，提出了在一类边界条件下预计未来水头的近似解析解。
The hydrogeological conditions are complicated there. An approximate analytic solution has been derived to estimate the future groundwater head on the first kind boundaries.
作为具体问题，采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。
As an example, an approximate analytic solution of nonlinear vibration for a plate strip in lateral magnetic field is obtained by the multi-scale method.
根据陈宁馨方程的近似解析解，导出了一个适用于精密精馏板式塔的简捷设计方程。
In this paper a short-cut design equation that applies to plate column for close-boiling fractionation is developed based on the approximate analytical solutions of Ning Hsing Chen's equations.
利用最小势能原理推导了肋拱桥结构在外荷载作用下侧倾稳定临界力的近似解析解。
With the principle of the minimum potential energy, an analytical solution for the lateral critical bucking Lord of tied-arch Bridges is studied.
本文基于有限解析法的基本思想，用单元内插值函数近似地代替单元内的近似解析解。
Based on the idea of finite analytic method, an interpolation function is used in place of the analytic solution, and a mathematical model is established.
给出了一类超低频标准振动台非线性运动方程的两种近似解析解——非共振解法和共振解法。
This paper presents two kinds of approximate analytical solution, non-resonance solution and resonance solution, of non-linear dynamic equation based on a type of ultra-low frequency vibrator.
给出了用切比雪夫多项式方法，求时滞系统的无穷时间线性二次型反鐀控制律的近似解析解的新方法。
A new algorithm derived from Chebyshev polynomials is presented for the approximate analytic solution of infinite-time linear-quadratic optimal feedback control law for time-delay systems.
第五章介绍美式期权的近似解析解，并在著名的BAW公式上进行修正，得出新的公式并进行数值试验。
Analytic approximation method is introduced in the chapter five and we make an adjustment of BAW formula.
阐述利用最新提出的同伦分析方法求解有正阻尼的强非线性振动方程，得到了该方程的六阶近似解析解。
In this paper, the sixth-order approximate analytical solutions of the strong nonlinear oscillation with positive damping are obtained by using newly developed homotopy analysis method.
采用广义牛顿粘度公式，得到了振动力场作用下的异向双螺杆挤出机螺棱侧间隙内的速度分布近似解析解。
The approximate analytical solution of the velocity distribution in the side gap of the counter-rotating twin screw extruder is obtained by means of the generalized Newtonian viscosity.
用算符分解算法(AOM)得到了系统的近似解析解，并研究了传动比和时变啮合刚度对拍击门槛转速的影响。
A-operator method (AOM) is used to study the influence of the speed ratio and time varying meshing stiffness on rattling threshold speed of the gear system.
为适应毛细管的工程设计要求，在绝热毛细管积分近似模型的基础上，提出壅塞流动下绝热毛细管长度的近似解析解。
With requirements of designing an adiabatic capillary tube in engineering, an approximate analytic solution to the tube length derived from the approximate integral model is developed.
分别用积分变换法和奇异摄动法，导出了数学模型在拉氏域内的解和时间域内的近似解析解，并用导得的解进行模型参数估值。
Parameters are evaluated by using an integral transform technique and a single perturbation technique. An improved method of moment is provided to treat experimental data.
从描述电子束运动的基本方程出发，引入一定条件下的近似，获得了一种实用的同轴二极管电流、电压与几何参数关系的近似解析解。
According to the Maxwell equations, an analytic solution related with coaxial diode current, applied voltage and geometry parameters is obtained by introducing certain approximation.
当介质的导热系数是温度的函数时，热传导方程是非线性偏微分方程，作者采用基尔霍夫变换把它变成拉普拉斯方程，于是可以找到原问题的近似解析解。
The nonlinear equation of heat conduction is transformed into a Laplace's equation by applying the Kirchhoff transformation, and an analytic approximate solution of the equation is derived.
从精确解出发，推导出最近文献中提出的“解析近似解”，并指出该近似解的适用条件。
The recently proposed "analytic approximation solution" is proved to be a good approximation to the corresponding analytic solution under some conditions.
本文用适当的多项式函数近似扩散光波导的高斯折射率分布函数，推导了导模有效折射率的解析形式渐近解。
The Gaussian index profile of a diffused optical waveguide is approximated by an appropriate polynomial, and the asymptotic solutions of the mode efficient index is derived in a analytical form.
带有提前支付特性的期权定价方程无法直接求出解析解，而传统的近似方法有其局限性。
No analytic formula have been solved from mortgage pricing equation with prepayment, and approximation methods limited in their application.
采用摄动法求得了其近似解，得到了载流梁在磁场中的横向固有振动频率及位移解析表达式。
The perturbation method was employed to get the control equation's approximate solution. The analytical expressions of beam's natural lateral vibration frequency and displacement were derived.
采用加权平均法可以得到该方程的近似的解析解，同时提高了计算精度。
The analytical approximate solution of the equation is been obtained and the calculated precision is improved simultaneously by using the Weighted Average Method.
对一类带耗散项非线性波动方程进行了研究，用“参数微分法”，得到其解析近似解。
This paper Studies nonlinear wave equation with dissipation items, reaching an approximate solution in the method of parameter differentiation.
对一类带耗散项非线性波动方程进行了研究，用“参数微分法”，得到其解析近似解。
This paper Studies nonlinear wave equation with dissipation items, reaching an approximate solution in the method of parameter differentiation.
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