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山东理工大学学报（自然科学版） 산동리공대학학보（자연과학판）
JOURNAL OF SHANDONG UNIVERSITY OF TECHNOLOGY(SCIENCE AND TECHNOLOGY)
2013年 6期 1-6 ,共6页

李慧玲%李功胜%贾现正%池光胜李慧玲%李功勝%賈現正%池光勝

리혜령%리공성%가현정%지광성

时间分数阶导数%二维对流扩散%多点源%反问题%最佳摄动量正则化算法%数值模拟時間分數階導數%二維對流擴散%多點源%反問題%最佳攝動量正則化算法%數值模擬
시간분수계도수%이유대류확산%다점원%반문제%최가섭동량정칙화산법%수치모의
time fractional derivative%2-D advection diffusion%multi-point sources%inverse prob-lem%optimal perturbation regularization algorithm%numerical simulation

对于一类带有多个点源的二维反常扩散问题，基于Caputo意义下时间分数阶导数的离散，给出了一个有限差分求解格式。在已知点源个数及位置的前提下，根据终止时刻的浓度观测数据，应用最佳摄动量正则化算法对源强度识别反问题进行了有效的数值反演，并讨论了正则参数、分数微分阶数及数据扰动等因素对反演算法的影响。
대우일류대유다개점원적이유반상확산문제，기우Caputo의의하시간분수계도수적리산，급출료일개유한차분구해격식。재이지점원개수급위치적전제하，근거종지시각적농도관측수거，응용최가섭동량정칙화산법대원강도식별반문제진행료유효적수치반연，병토론료정칙삼수、분수미분계수급수거우동등인소대반연산법적영향。
A finite difference scheme is introduced to solve the 2-D time fractional diffusion equa-tion with multiple point sources based on Caputo’s discretization to the time fractional derivative , and numerical test is presented .Furthermore ,the optimal perturbation regularization algorithm is applied to determine the magnitudes of the multi-point sources using measurements at the final time .Numerical inversions are performed to demonstrate the effectiveness of the proposed algo-rithm ,and influences of the regularization parameter ,the fractional order and the data noises on the inversion algorithm are discussed .