 |
 |
 |
 |
 |
 |
||
 |
 |
 |
 |
 |
| 5 | 1/1 | 返回列表 |
| 查看: 2287 | 回復(fù): 7 | ||||
| 當(dāng)前只顯示滿足指定條件的回帖，點(diǎn)擊這里查看本話題的所有回帖 | ||||
yuanjian1987木蟲 (正式寫手)
|
[求助]
分?jǐn)?shù)階微分方程Predictor-corrector PECE，程序怎么運(yùn)行呢？
|
|||
|
附件是老外編寫的程序，但是我不會(huì)運(yùn)行，誰(shuí)能舉個(gè)例子運(yùn)行一下呢？ 比如 D^q1=x^2+xy; D^q2=-x^2-2y; fdefun需要單獨(dú)編一個(gè)m文件嗎？ 里面有好多function，需要將它們單獨(dú)編一個(gè)m文件嗎？ 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 |
回復(fù)此樓» 本帖附件資源列表
-
歡迎監(jiān)督和反饋：小木蟲僅提供交流平臺(tái)，不對(duì)該內(nèi)容負(fù)責(zé)。
本內(nèi)容由用戶自主發(fā)布，如果其內(nèi)容涉及到知識(shí)產(chǎn)權(quán)問題，其責(zé)任在于用戶本人，如對(duì)版權(quán)有異議，請(qǐng)聯(lián)系郵箱：xiaomuchong@tal.com - 附件 1 : fde12.m
2013-11-24 20:58:59, 9.11 K
» 猜你喜歡
一志愿華東師范大學(xué)有機(jī)化學(xué)專業(yè)，初試351分，復(fù)試被刷求調(diào)劑!
已經(jīng)有4人回復(fù)
-
298求調(diào)劑
已經(jīng)有4人回復(fù)
-
材料學(xué)碩333求調(diào)劑
已經(jīng)有11人回復(fù)
-
0856求調(diào)劑
已經(jīng)有7人回復(fù)
-
356求調(diào)劑
已經(jīng)有3人回復(fù)
-
332求調(diào)劑
已經(jīng)有7人回復(fù)
-
348求調(diào)劑
已經(jīng)有4人回復(fù)
-
305求調(diào)劑
已經(jīng)有8人回復(fù)
-
一志愿北京化工大學(xué)材料與化工（085600）296求調(diào)劑
已經(jīng)有13人回復(fù)
-
調(diào)劑310
已經(jīng)有9人回復(fù)
» 本主題相關(guān)價(jià)值貼推薦，對(duì)您同樣有幫助:
- 分?jǐn)?shù)階微分方程的求解（用差分法，matlab編程求解）
已經(jīng)有9人回復(fù)
- 【討論】分?jǐn)?shù)階微分方程
已經(jīng)有28人回復(fù)
Math露珠
木蟲 (知名作家)
- 應(yīng)助: 10 (幼兒園)
- 金幣: 7841.6
- 散金: 2548
- 紅花: 123
- 沙發(fā): 33
- 帖子: 8870
- 在線: 885.7小時(shí)
- 蟲號(hào): 4010226
- 注冊(cè): 2015-08-07
- 專業(yè): 常微分方程與動(dòng)力系統(tǒng)
|
你好，請(qǐng)問Diethelm的書（Springer 2010）全名是The analysis of fractional differential equations: An application-oriented exposition嗎?沒有搜到，能否分享一下，謝謝 發(fā)自小木蟲Android客戶端 |
7樓2017-10-21 00:50:32
feixiaolin
榮譽(yù)版主 (文壇精英)
-
專家經(jīng)驗(yàn): +518 - 應(yīng)助: 942 (博后)
- 貴賓: 1.275
- 金幣: 3880
- 散金: 58785
- 紅花: 532
- 沙發(fā): 11
- 帖子: 24215
- 在線: 2601.8小時(shí)
- 蟲號(hào): 2139575
- 注冊(cè): 2012-11-21
- 專業(yè): 光學(xué)信息獲取與處理
- 管轄: 數(shù)學(xué)
|
alpha：FDE的階次，必須為正. fdefun 是標(biāo)量T和向量Y定義的指向矢量場(chǎng)FDE的函數(shù)函數(shù)句柄，F(xiàn)DEFUN(T,Y) 必須返回一個(gè)列向量。. t0,tfinal: 參數(shù)t的初始值、終值. y0：一個(gè)矩陣，其行等于該問題的大�。ㄒ驳扔谛蠪DEFUN的輸出數(shù)） param：參數(shù)個(gè)數(shù). mu：校正迭代參數(shù)選擇參數(shù). 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：控制誤差. h:從N = ceil((tfinal-t0)/h) 看，h是時(shí)間跨距，N是評(píng)估解的時(shí)間點(diǎn)的數(shù)目。 FDE12詳見 http://www.mathworks.cn/matlabce ... ferential-equations |
2樓2013-11-24 21:44:53
感謝參與，應(yīng)助指數(shù) +1
|
本帖內(nèi)容被屏蔽 |
3樓2013-11-25 05:58:36
|
本帖內(nèi)容被屏蔽 |
4樓2013-11-25 06:06:27
| 最具人氣熱帖推薦 [查看全部] | 作者 | 回/看 | 最后發(fā)表 | |
|---|---|---|---|---|
|
[考研] 材料學(xué)碩333求調(diào)劑 +11 | 北道巷 2026-03-24 | 11/550 |
|
|---|---|---|---|---|
|
|
[考研] 329求調(diào)劑 +7 | 星野? 2026-03-26 | 7/350 |
|
|
|
[考研] 一志愿北京理工大學(xué)本科211材料工程294求調(diào)劑 +6 | mikasa的圍巾 2026-03-28 | 6/300 |
|
|
[考研] 求調(diào)劑一志愿海大，0703化學(xué)學(xué)碩304分，有大創(chuàng)項(xiàng)目，四級(jí)已過 +7 | 幸運(yùn)哩哩 2026-03-22 | 11/550 |
|
|
|
[考研] 085600，材料與化工321分求調(diào)劑 +9 | 大饞小子 2026-03-28 | 9/450 |
|
|
|
[考研] 311求調(diào)劑 +9 | lin0039 2026-03-26 | 9/450 |
|
|
|
[考研] 【求調(diào)劑】085601材料工程專碩 | 總分272 | +6 | 腳滑的守法公民 2026-03-27 | 6/300 |
|
|
|
[考研] 277跪求調(diào)劑 +5 | 1915668 2026-03-27 | 9/450 |
|
|
|
[考研] 085404求調(diào)劑，總分309，本科經(jīng)歷較為豐富 +4 | 來財(cái)aa 2026-03-25 | 4/200 |
|
|
|
[考研] 287求調(diào)劑 +10 | land xuxu 2026-03-26 | 10/500 |
|
|
|
[考研] 348求調(diào)劑 +4 | 小懶蟲不懶了 2026-03-27 | 5/250 |
|
|
|
[考研] 調(diào)劑 +3 | 李嘉圖·S·路 2026-03-27 | 3/150 |
|
|
|
[考研] 324求調(diào)劑 +8 | hanamiko 2026-03-26 | 10/500 |
|
|
|
[考研] 342求調(diào)劑 +3 | 加油a李zs 2026-03-26 | 3/150 |
|
|
|
[考研]
 085602 289分求調(diào)劑
+8
|
WWW西西弗斯 2026-03-24 | 8/400 |
|
|
|
[考研] 求調(diào)劑 +3 | 李李不服輸 2026-03-25 | 3/150 |
|
|
|
[考研] 調(diào)劑 +4 | 13853210211 2026-03-24 | 4/200 |
|
|
|
[考研] 材料專碩331求調(diào)劑 +4 | 鮮當(dāng)牛 2026-03-24 | 4/200 |
|
|
|
[考研] 一志愿河北工業(yè)大學(xué)0817化工278分求調(diào)劑 +7 | jhybd 2026-03-23 | 12/600 |
|
|
|
[考研] 269求調(diào)劑 +4 | 我想讀研11 2026-03-23 | 4/200 |
|