数值积分和微分方程偏pdepe

1、对一维抛物-椭圆型 PDE 的初始边界值问题求解 - MATLAB pdepe - MathWorksIIKRKXGZOTM ZNK VGIK UL KTMOTKKXOTM GTJ 试用产品更共 对一维抛物-椭圆型 PDE 对一维抛物-椭圆型 PDE 的初始边界值问题求解 - MATLAB pdepe - MathWorksIIKRKXGZOTM ZNK VGIK UL KTMOTKKXOTM GTJ 试用产品更共 对一维抛物-椭圆型 PDE 的初始边界值问题求sol = sol=sol,tsol,sole,te,ie=澞m 2m x0 x1 x0 x1xn澞xmesh = 3 0 1C xe

2、shtpannt0t1tf澞tspan 3 pdepeRelTol澝AbsTol澝NormControl澝InitialStep澝MaxStep Events澞 澞 sol = pdepe(m,pdefun,icfun,bcfun,xmesh,tspan) D 澞pdefun澝 bcfun 澞 function_handle tspan 澞pdepe xmesh pdefun澝icfun bcfun 澞pdepe 2 -D 澞.) 澞9 澞 澞 - 2DAAD 澞凥DAAD 澞 澞 澞 / ? 澞 D 澞 file:/C|/Users/Administrator/Desktop/pdepe.h

3、tm2014/10/2 搜索最新文对一维抛物-椭圆型 PDEpdepe - MathWorks Z # G # H W 澞 L 对一维抛物-椭圆型 PDEpdepe - MathWorks Z # G # H W 澞 L 澞 V sol = pdepe(m,pdefun,icfun,bcfun,xmesh,tspan)mS 澞xmesh(1xmesh(end) G H tspan(1tspan(end) Z ZL澞 pdefun I澝L Y 澞 c,f,s = x t u dudx 澞c澝f s 澞c icfun澞 u = xicfun u bcfun V W澞 pl,ql,pr,qr = l

4、 l # G r r# H l l V W l r r澞S$G# L G#澞e l l 澞el澞O # i# sol:i iijk#lki Z # tspanj xmeshk Ouisolji tspanj xmesh(i澞 pdeval xmeshO澞 pdevalsol=pdepe(m,pdefun,icfun,bcfun,xmesh,tspan,options) odeset 澞 5*+ pdepeRelTol澝AbsTol澝NormControl澝InitialStep MaxStep澞 options 澞 odeset Events g(t,u(x,t 澞eventsvalue,is

5、terminal,direction = events(m,t,xmesh,umesh)xmesh umesh澞 pdeval澞 / value(i ISTERMINAL(I1 澞direction(i) 0 澞 tsol tspan 澞SOL(j,: T(j澞TE 澞SOLE(j TE(j IE I = SL,) SA() MH l XO UOUT UOUT,DUOUTDX= PDEVAL(M,XMESH,UI,XOUT) 澞 6*+ 澝 Z 6*+澞 pdepe O 澞 澞对一维抛物-椭圆型 PDEpdepe - MathWorksfunction m = x=linspace(0,1,2

6、0); t = linspace(0,2,5);sol = 对一维抛物-椭圆型 PDEpdepe - MathWorksfunction m = x=linspace(0,1,20); t = linspace(0,2,5);sol = % Extract thesolutioncomponentasu. u = sol(:,:,1);%Asurfaceplotisoftenagoodwaytostudyasolution. title(Numerical solution computed with 20 mesh poxlabel(Distance x)ylabel(Time % A so

7、lution profile csobeilluminating. title(Solutionatt=2) xlabel(Distance x) %functionc,f,s=pdex1pde(x,t,u,DuDx) c = pi2;f=DuDx; s = 0;%functionu0=pdex1ic(x) u0 = sin(pi*x);%functionpl,ql,pr,qr=pdex1bc(xl,ul,xr,ur,t) pl = ul;ql = pr=pi*exp(-t); qr = 1; pdex1pde澝pdex1ic 6*+ t t2对一维抛物-椭圆型 PDEpdepe - Math

8、Works 澞 6*+ 澞 Z 对一维抛物-椭圆型 PDEpdepe - MathWorks 澞 6*+ 澞 Z 6*+ , _ # _ KV Z 澞 澞 澞 functionpdex4 m = 0;x = 0 0.005 0.01 0.05 0.1 0.2 0.5 0.7 0.9 0.95 0.99 0.995 t = 0 0.005 0.01 0.05 0.1 0.5 1 1.5 sol=pdepe(m,pdex4pde,pdex4ic,pdex4bc,x,t); u1 = sol(:,:,1);u2 = 对一维抛物-椭圆型 PDEpdepe - MathWorksxlabel(Dista

9、ncex) ylabel(Time t)xlabel(Distancex) ylabel(Time t)%functionc,f,s=pdex4pde(x,t,u,DuDx) c = 1; 1;f 对一维抛物-椭圆型 PDEpdepe - MathWorksxlabel(Distancex) ylabel(Time t)xlabel(Distancex) ylabel(Time t)%functionc,f,s=pdex4pde(x,t,u,DuDx) c = 1; 1;f = 0.024; 0.17 .* y = u(1) - F=exp(5.73*y)-exp(-11.47*y); s =

10、 -F; F;%functionu0=pdex4ic(x); u0 = 1; 0;%functionpl,ql,pr,qr=pdex4bc(xl,ul,xr,ur,t) pl = 0; ul(2);ql = 1; pr=ur(1)-1;0; qr = 0; 1; pdex4pde澝pdex4ic pdex4bc 6* xmesh tspan pdepe pdepe 5*+ 澞对一维抛物-椭圆型 PDEpdepe - MathWorksAC9QKKR 8 * GTJ3 XOTY 3KZNUJLUXZNK对一维抛物-椭圆型 PDEpdepe - MathWorksAC9QKKR 8 * GTJ3 XOTY 3KZNUJLUXZNK9VGZOGR*OYIXKZOGZOUTUL6GXGHUROI+WGZOUTYOT5TK9VGIKGXOGHR