1) four order parabolic equation
四阶抛物型方程
1.
At present,some researchers have got a lot of good numerical solutions for the periodic initial value problem of four order parabolic equation: such as finite difference method,finite elements method,spectral Galerkin method and so on.
本文首先将四阶抛物型方程转化为一个二阶的偏微分方程组,然后对时间项采用子域精细积分的方法、空间项采用三次样条基本公式进行离散,得到了一个含参数α>0(αh)的无条件稳定的差分格式,所得到的差分方程为五点、两层隐格式,它的局部截断误差为O(2τ+α2τ+h4)。
2.
To solve four order parabolic equation,a class of three-layer implicit different schemes containing double parameters are constructed.
对四阶抛物型方程构造一族新的含双参数三层隐式差分格式,并证明该族格式对任意非负参数都是绝对稳定,并且其局部截断误差达到O[(Δt)2+(Δx)8],通过数值例子表明该格式是有效的。
3.
For solving four order parabolic equation ut+ 4ux 4=0, the author advances two new classes of three layered implicit difference scheme with coefficient matrix of tridiagonal type.
为了解四阶抛物型方程 u t+ 4u x4=0 ,建立两类新的、具三对角线型系数矩阵的三层隐式差分格式 其局部截断误差阶均为O(τ2 +h2 +(τh) 2 ) ,且都是绝对稳定的 ,并可用追赶法容易地求解 数值例子表明这些格式是有效
2) four-order parabolic equation
四阶抛物型方程
1.
New three-layer implicit difference schemes with parameters are proposed for solving four-order parabolic equation.
本文对四阶抛物型方程 04=+xt 构造了一族含参数三层隐式差分格式。
2.
For solving four-order parabolic equation,a new group of explicit difference scheme contains Du Fort-Frankel difference schemes.
对四阶抛物型方程构造一族新的含参数三层显式差分格式 。
3.
A three-level explicit difference scheme is proposed fo r solving four-order parabolic equation.
给出解四阶抛物型方程的一个新的显式差分格式 ,其截断误差和稳定性条件分别为O(△t2 +△x6 )和r=△t/△x4 <1/ 16。
3) fourth order parabolic equation
四阶抛物型方程
1.
In this paper,several new difference schemes for solving fourth order parabolic equation are developed by using dissipative term,and their orders of the local trumcation error and stability are discussed.
利用加耗散项的方法,提出解四阶抛物型方程的若干新的差分格式,研究它们的局部截断误差阶及稳定性。
2.
In this paper,we mainly consider the large time behavior of global solutions to the Cauchy problem of fourth order parabolic equation in one dimension space:with f(u) satisfyingHere are our main results:(i) Suppose the initial data satisfies .
本文主要考虑一维空间中四阶抛物型方程的Cauchy问题整体解u=u(x，t)的大时间行为。
3.
In this paper,we consider the large time behavior and the time-decay rate of global solutions to the Cauchy problem of fourth order parabolic equation in one dimension space: ■with f(u)satisfying f(u)∈C~1(■),|f(u)|≤C|u|~q,q>5/2.
本文考虑一维空间中四阶抛物型方程Cauchy问题■的整体解u=(x,t)的大时间渐近行为和时间衰减速率,其中
4) four order parabolic equations
四阶抛物型方程
1.
A two-level explicit finite difference scheme of high accuracy for solving four order parabolic equations is presented,the stability condition of the presented scheme is r=τ/h4≤264/3601 and the truncation order iso(τ2+h8).
给出了一个求解四阶抛物型方程高精度两层显式差分格式,证明了其截断误差为O(τ2+h8),稳定性条件为r=τ/h4≤264/3601。
2.
A ten-point two-level explicit finite difference scheme to solve four order parabolic equations is presented,and it is demonstrated that the stability condition of the presented scheme is ο(τ2+h4) and the truncation order is r=τh4≤79384.
给出了一个求解四阶抛物型方程的两层十点显式差分格式,证明了其截断误差为ο(τ2+h4),稳定性条件为r=hτ4≤37894。
5) Nonlinear parabolic equation of fourth order
四阶非线性抛物型方程
6) nonlinear parabolic equations with the forth order
非线性四阶抛物型方程
补充资料：抛物型偏微分方程
| 抛物型偏微分方程 parabolic type，partial differential equation of 偏微分方程的一类。最典型的是热传导方程  （a＞0） （1）基本解是点热源的影响函数。若在t＝0时在（ξ，η，ζ）处给定单位点热源，即u0（x0，y0，z0，0）＝δ（ξ，η，ζ）（δ为狄拉克函数），则当t＞0时便引起在R3的温度分布，这就是基本解。用傅里叶变换可得到它的表达式  热传导方程初值问题的解可用基本解叠加而成，即  的解为  极值原理：一个内部有热源的传导过程，它的最低温度一定在边界上或初始时刻达到。更强的结论是 ：如果t＝T时在Ω内某一点达到最低温度 ，则在这个时刻以前（t＜T时）u≡常数 ；又：若最低温度在t＝T时边界¶Ω上某点P达到，则在这点上  ｜P，Τ＜0（n为外法线方向）。 |
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