| 查看: 2618 | 回复: 7 | ||||
| 当前只显示满足指定条件的回帖，点击这里查看本话题的所有回帖 | ||||
yuanjian1987木虫 (正式写手)
|
[求助]
分数阶微分方程Predictor-corrector PECE，程序怎么运行呢？
|
|||
|
附件是老外编写的程序，但是我不会运行，谁能举个例子运行一下呢？ 比如 D^q1=x^2+xy; D^q2=-x^2-2y; fdefun需要单独编一个m文件吗？ 里面有好多function，需要将它们单独编一个m文件吗？ Description of FDE12 FDE12 solves an initial value problem for a nonlinear differential equation of fractional order (FDE). The code implements the predictor-corrector PECE method of Adams-Bashforth-Moulton type described in [1]. [T,Y] = FDE12(ALPHA,FDEFUN,T0,TFINAL,Y0,h) integrates the initial value problem for the FDE, or the system of FDEs, of order ALPHA > 0 D^ALPHA Y(t) = FDEFUN(T,Y(T)) Y^(k)(T0) = Y0(:,k+1), k=0,...,m-1 where m is the smallest integer greater than ALPHA and D^ALPHA is the fractional derivative according to the Caputo's definition. FDEFUN is a function handle corresponding to the vector field of the FDE and for a scalar T and a vector Y, FDEFUN(T,Y) must return a column vector. The set of initial conditions Y0 is a matrix with a number of rows equal to the size of the problem (hence equal to the number of rows of the output of FDEFUN) and a number of columns depending on ALPHA and given by m. The step-size H>0 is assumed constant throughout the integration. [T,Y] = FDE12(ALPHA,FDEFUN,T0,TFINAL,Y0,H,PARAM) solves as above with the additional set of parameters for the FDEFUN as FDEFUN(T,Y,PARAM). [T,Y] = FDE12(ALPHA,FDEFUN,T0,TFINAL,Y0,H,PARAM,MU) solves the FDE with the selected number MU of multiple corrector iterations. The following values for MU are admissible: MU = 0 : the corrector is not evaluated and the solution is provided just by the predictor method (the first order rectangular rule); MU > 0 : the corrector is evaluated by the selected number MU of times; the classical PECE method is obtained for MU=1; MU = Inf : the corrector is evaluated for a certain number of times until convergence of the iterations is reached (for convergence the difference between two consecutive iterates is tested). The defalut value for MU is 1 [T,Y] = FDE12(ALPHA,FDEFUN,T0,TFINAL,Y0,H,PARAM,MU,MU_TOL) allows to specify the tolerance for testing convergence when MU = Inf. If not specified, the default value MU_TOL = 1.E-6 is used. FDE12 is an implementation of the predictor-corrector method of Adams-Bashforth -Moulton studied in [1]. Convergence and accuracy of the method are studied in [2]. The implementation with multiple corrector iterations has been proposed and discussed for multiterm FDEs in [3]. In this implementation the discrete convolutions are evaluated by means of the FFT algorithm described in [4] allowing to keep the computational cost proportional to N*log(N)^2 instead of N^2 as in the classical implementation; N is the number of time-point in which the solution is evaluated, i.e. N = (TFINAL-T)/H. The stability properties of the method implemented by FDE12 have been studied in [5]. [1] K. Diethelm, A.D. Freed, The Frac PECE subroutine for the numerical solution of differential equations of fractional order, in: S. Heinzel, T. Plesser (Eds.), Forschung und Wissenschaftliches Rechnen 1998, Gessellschaft fur Wissenschaftliche Datenverarbeitung, Gottingen, 1999, pp. 57-71. [2] K. Diethelm, N.J. Ford, A.D. Freed, Detailed error analysis for a fractional Adams method, Numer. Algorithms 36 (1) (2004) 31-52. [3] K. Diethelm, Efficient solution of multi-term fractional differential equations using P(EC)mE methods, Computing 71 (2003), pp. 305-319. [4] E. Hairer, C. Lubich, M. Schlichte, Fast numerical solution of nonlinear Volterra convolution equations, SIAM J. Sci. Statist. Comput. 6 (3) (1985) 532-541. [5] R. Garrappa, On linear stability of predictor-corrector algorithms for fractional differential equations, Internat. J. Comput. Math. 87 (10) (2010) 2281-2290. Copyright (c) 2011-2012, Roberto Garrappa, University of Bari, Italy garrappa at dm dot uniba dot it Revision: 1.2 - Date: July, 6 2012 |
回复此楼» 本帖附件资源列表
-
欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com - 附件 1 : fde12.m
2013-11-24 20:58:59, 9.11 K
» 猜你喜欢
售SCI一区T0P文章，我:8.O.55.1.O54,科目全,可伽急
已经有6人回复
-
售SCI文章，我:8O.5.5.1O.54,科目全,可十急
已经有7人回复
-
售SCI一区文章，我:8O5.5.1.O5.4,科目全,可伽急
已经有8人回复
-
售一区SCI文章T0P，我:8O.551.O54,科目全,可十急
已经有3人回复
-
售SCI一区T0P文章，我:8.O.55.1.O.54,科目齐全,可+急
已经有5人回复
-
售SCI-T0P文章，我:8O.5.5.1.O.54,科目齐全,可+急
已经有7人回复
-
售SCI文章，我:8O5.5.1.O.54,科目齐全,可+急
已经有7人回复
-
售SCI一区T0P文章，我:8.O.55.1.O54,科目全,可伽急
已经有6人回复
-
售一区SCI文章T0P，我:8O.551.O54,科目全,可十急
已经有6人回复
-
售SCI一区T0P文章，我:8.O.55.1.O54,科目全,可伽急
已经有8人回复
» 本主题相关价值贴推荐，对您同样有帮助:
- 分数阶微分方程的求解（用差分法，matlab编程求解）
已经有9人回复
- 【讨论】分数阶微分方程
已经有28人回复
感谢参与，应助指数 +1
|
本帖内容被屏蔽 |
3楼2013-11-25 05:58:36
feixiaolin
荣誉版主 (文坛精英)
-
专家经验: +518 - 应助: 942 (博后)
- 贵宾: 1.275
- 金币: 3896
- 散金: 58785
- 红花: 532
- 沙发: 11
- 帖子: 24218
- 在线: 2601.8小时
- 虫号: 2139575
- 注册: 2012-11-21
- 专业: 光学信息获取与处理
- 管辖: 数学
|
alpha：FDE的阶次，必须为正. fdefun 是标量T和向量Y定义的指向矢量场FDE的函数函数句柄，FDEFUN(T,Y) 必须返回一个列向量。. t0,tfinal: 参数t的初始值、终值. y0：一个矩阵，其行等于该问题的大小（也等于行FDEFUN的输出数） param：参数个数. mu：校正迭代参数选择参数. MU = 0 : the corrector is not evaluated and the solution is provided just by the predictor method (the first order rectangular rule); MU > 0 : the corrector is evaluated by the selected number MU of times; the classical PECE method is obtained for MU=1; MU = Inf : the corrector is evaluated for a certain number of times until convergence of the iterations is reached (for convergence the difference between two consecutive iterates is tested). The defalut value for MU is 1 mu_tol：控制误差. h:从N = ceil((tfinal-t0)/h) 看，h是时间跨距，N是评估解的时间点的数目。 FDE12详见 http://www.mathworks.cn/matlabce ... ferential-equations |
2楼2013-11-24 21:44:53
|
本帖内容被屏蔽 |
4楼2013-11-25 06:06:27
yuanjian1987
木虫 (正式写手)
- 应助: 20 (小学生)
- 金币: 4246.9
- 散金: 20
- 红花: 6
- 帖子: 997
- 在线: 118.7小时
- 虫号: 1921345
- 注册: 2012-08-02
- 性别: GG
- 专业: 电能储存与节电技术
5楼2013-12-04 10:26:46
