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［］（1986-），，，，。20097Jul.2009244JournalofXianyangNormalUniversityVol.24No.4，[1]，[2]，，。，，。MATLAB[3]，。,,、。，，MATLAB[4，5]。MATLAB[6]，、，。坠u坠t=a2坠2u坠x2，，，，、；，。，、、；，[7](FDM)，。FDM，。，：坠u坠t=a2坠2u坠x2，0＜l,t＞0u|x=0=0,u|x=l=0,t＞0u|x=0=sinπxl!,0＜x＜#%%$%%&l，，。Taylor，，。1，；；，，，，。[8,9]。：(1)；(2)；(3)；(4)。MATLAB(，710055)：，。，MATLAB。，MATLAB，。：；；MATLAB：O552：A：1672-2914（2009）04-0027-03·28·242，（x-t），△x=l/M,△t=T/N,，，，。u(x,t)t[10]：坠u坠t≈unj-un-1j△t，t[10]：坠2u坠x2≈unj+1-2unj+unj-1(△x)2，。：unj-un-1j△t=a2unj+1-2unj+unj-1(△x)2。：r=a2·△t(△x)2，（1＋2r)unj-r·unj+1-r·unj-1=un-1j。：1+2r-r00…0-r1＋2r-r0…000-r1＋2r-r00…00-r1＋2＋＋＋＋＋＋＋＋＋＋＋＋＋＋r（M-1)×（M-1)un1un2unM-2unM-1＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋=un-11+r·un0un-12un-1M-2un-1M-1+r·unM＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋＋3MATLAB%clear;clc;formatshortea=input('a：');l=input('l：');M=input('[0,l]M：');ot=input('ot：');n=input('n：');ox=l/M;x0=zeros(M+1,1);forii=1:Mx0(ii+1)=ii*ox;endu=sin(pi*x0/l);%t=0u(x,t)r=a^2*ot/(ox)^2;forii=1:n%B=zeros(M-1,1);%A=zeros(M-2,1);%C=zeros(M-2,1);%S=zeros(M-1,1);%forii=1:M-2B(ii)=1+2*r;A(ii)=-r;C(ii)=-r;S(ii)=u(ii+1,1);endB(M-1)=1+2*r;S(M-1)=u(M,1);u(1,2)=0;u(M+1,2)=0;S(1,1)=S(1,1)+r*u(1,2);S(M-1,1)=S(M-1,1)+r*u(M+1,2);%S(1)=S(1)/B(1);T=B(1);k=2;whilek~=MB(k-1)=C(k-1)/T;T=B(k)-A(k-1)*B(k-1);S(k)=(S(k)-A(k-1)*S(k-1))/T;k=k+1;endk=1;whilek~=M-1S(M-1-k)=S(M-1-k)-B(M-1-k)*S(M-k);k=k+1;endu(2:M,2)=S;%uu(:,1)=u(:,2);%end%，uforx=0:Mu(x+1,2)=exp(-(pi*a/l)^2*n*ot)*sin(pi*x*ox/l);tTn+1nn-10j-1jj+1lx(j-1,n)(j-1,n)(j,n)(j+1,n)(j,n-1)→←△x△t↓↑1…………………誗誗誗誗4：MATLAB·29·end%ez=zeros(M-1,1);forii=2:Mez(ii-1)=abs(u(ii,1)-u(ii,2))/u(ii,2);endE=max(ez);fprintf(':\n');disp(u);fprintf('：');disp([num2str(E*100)'%']);%plot(x0,u(:,1),'r:',x0,u(:,2),'b-');legend('','')xlabel('x'),ylabel('u(x,t)')title('')。4：a：1l：1［0，l］M：8ot：0.001n：901。：1.5723%。ξj||ξj||燮C||ξ0||,(j叟1)(ξ0),，1，，2。5MATLAB，，，MATLAB，。：[1],,.[J].,2005,19(4):76-80.[2]，，.[J].(），2007,20(3)：12-14.[3]StephenJ.Chapman.MATLAB[M].，，.：，2008.[4].MATLAB[J].，2006,20(4):12-13.[5]，.MATLAB[J].()，2003,22(4):21-27.[6].[J].,2008,24(2):31-36.[7].[J].()，2004,34(3):16-18.[8]，.MATLAB[J].，2005，18(4):61-64.[9]，.MATLAB[J].，2008，21(3):1-2.[10].[M].：，1979.1001.5990e-0011.5990e-0012.9546e-0012.9088e-0013.8603e-0013.8006e-0014.1784e-0014.1137e-0013.8603e-0013.8006e-0012.9546e-0012.9088e-0011.5990e-0011.5742e-00105.0378e-017(36)HeatConductionEquationFiniteDifferenceMethodtoAchievetheMATLABSHICe（SchoolofScience,Xi'anUniversityofArchitectureandTechnology,Xi'an,Shaanxi710055,China）Abstract:Forboundedhomogeneousheatconductionequationofthemixedproblem,separationofvariablesmethodusedisoftenverycomplex.Inordertobetterunderstandtheheatconductionequation,itisusefultoapplytheMATLABsoftwareequationbyimagesexpression.Thoughwhichtransformsthroughtheregion,whichispro-grammingusingMATLABheatconductionequationofacertainregionofthefinitedifferencemethod,andnumer-icalmethoddemonstratesthefeasibilityandstability.Keywords:heatconductionequation;finitedifference;MATLAB·36·24tionoforganicpollutantsonnitrogenandfluorideco-dopedTiO2photocatalyst[J].JournalofEnvironmentalSciences,2005,17(1):76-80.[9]OhnoT,AkiyoshiM.PreparationofS-dopedTiO2photocata-lystsandtheirphotocatalyticactivitiesundervisiblelight[J].AppliedCatalysisA:2004,265:115-121.[10]UmebayashiT,YamakiT.Analysisofelectronicstructuresof3dtransitionmetal-dopedTiO2basedonbandcalculations[J].JournalofPhysicsandChemistryofSolids,2002,63:1909-1920.[11]BalachandranU,ErorNG.Laser-inducedvapourphasesyn-thesisoftitaniumdioxide[J].JournalofSolidStateChem-istry,1982,42:276-282.[12]MelendresCA.RamanspectroscopyofnanophaseTiO2Source[J].MaterialsResearchBulletin,1989，4(5):1246-1250.[13]ParkerJC,SiegelRW.RamanmicroprobestudyofnanophaseTiO2andoxidation-inducedspectralchanges[J].MaterialsResearchBulletin,1990,5(6):1246-1249.[14]AraiT,YanagidaM,KonishiY.Effficientcompleteoxida-tionofacetaldehydeintoCO2overCuBi2O4/WO3compositephotocatalystundervisibleandUVligntirradiation[J].Phys-icalChemistry,2007,111(21):7574-7577.PreparationofTiO2PhotocatalystCouplingDopedwithSandNElementsYUZhan-jiang，WANGXiao-fang(SchoolofChemistryandChemicalEngineering,XianyangNormalUniversity,Xianyang,Shaanxi712000,China)Abstract:UsingtetrabutyltitanateasTisource,glacialaceticacidasahydrolyzedinhibitorandDL-methion-ineasasmallmoleculedopant,aTiO2photocatalystcouplingdopedwithSandNnonmetallicelementswaspre-paredviaSol-Gelmethod.XPSanalysisshowsthatN2-incorporatesintotheTiO2crystallatticeandreplacedpartlyO2-,andthattheS4+andS2-alsoincorporateintotheTiO2crystallatticeandsubstitutepartialTi4+andO2-respec-tively.HencetheformationofSandNcoupling-dopingonTiO2getsachieved.XRDdiffractionindicatestheSandNcouplingdopedTiO2photocatalystsallexistinthephaseofanatase,whichdemonstratethatSandNcou-pling-dopingfeaturesstrongereffectonrestrainingtheTiO2crystalphasetransformationfromanatasetorutile.OpticalpropertyanalysispresentsthattheSandNcoupling-dopinghaseffectnotonlyonextendingabsorptionedgeofphotocatalysttovisiblelightregionbutonkeepingtheultravioletlightabsorptionnearlyunchanged.Keywords:photocatalyst;coupling-doping;titaniumdioxide;Sol-Ge