| function pdex9 | | m = 0; | | x = linspace(0,1); | | t = linspace(0,10000000000); | | sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t); | | u1 = sol(:,:,1); | | u2 = sol(:,:,2); | | u3 = sol(:,:,3); | | u4 = sol(:,:,4); | | %–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | figure | | plot(x,u1(end,:)) | | title(
′
u1(x,t)
′
) | | xlabel(
′
Distance x
′
) | | ylabel(
′
u1(x,1)
′
) | | %–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | figure | | plot(x,u2(end,:)) | | title(
′
u2(x,t)
′
) | | xlabel(
′
Distance x
′
) | | ylabel(
′
u2(x,2)
′
) | | % ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | figure | | plot(x,u3(end,:)) | | title(
′
u3(x,t)
′
) | | xlabel(
′
Distance x
′
) | | ylabel(
′
u3(x,3)
′
) | | %–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | figure | | plot(x,u4(end,:)) | | title(
′
u4(x,t)
′
) | | xlabel(
′
Distance x
′
) | | ylabel(
′
u4(x,4)
′
) | | %–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | function [c,f,s] = pdex4pde(x,t,u,DuDx) | | c = [0; 0; 0; 0]; | | f = [1; 1; 1; 1].* DuDx; | | r1 = 0.1; r2 = 0.1; r3 = 0.1; r4 = 0.1; r5 = 0.1; a = 0.1; b = 0.1; | | F1 = - r1 * u(1) - (r2 * u(1) * u(2))/(a * u(1)+u(2) * b); | | F2 = - (r3 * u(1) * u(2))/(a * u(1)+u(2) * b); | | F3 = ((r4/2) * u(1)); | | F4 = (r5 * u(1) * u(2))/(a * u(1)+u(2) * b); | | s = [F1; F2; F3; F4]; | | % ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | function u0 = pdex4ic(x) %create a initial conditions | | u0 = [1; 1; 0; 0]; | | % ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– | | function [pl,ql,pr,qr]= pdex4bc(xl,ul,xr,ur,t) %create a boundary conditions | | pl = [0; 0; ul(3); 0]; | | ql = [1; 1; 0; 1]; | | pr = [ur(1)-1; ur(2)-1; ur(3)-0; ur(4)-0]; | | qr = [0; 0; 0; 0]; |
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