Adding a known velocity (convection) term to reaction diffusion equation using bvp4c

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Jennifer Yang 2018-7-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/411041-adding-a-known-velocity-convection-term-to-reaction-diffusion-equation-using-bvp4c

I am trying to add a known velocity (10 m/s) to my steady state reaction diffusion equation although I'm a bit confused how to go about doing that.

This is my current code

    function simple_steady_state_bvp4c
    close all; clear all; clc;
    %Diffusion coefficient
    D_ij= 1*10^-6;
    %Initial concentration at x=0
    L0 = 1;
    %Total length
    x_f = 0.025;
    k_1 = 0.25;
    solinit = bvpinit(linspace(0,x_f,11),[0.5 0]);
    sol = bvp4c(@(x,y)odefcn(x,y,D_ij,k_1),@twobc,solinit);
    figure(1)
    plot(sol.x,(sol.y(1,:)),'LineWidth',1)
    title('Steady State')
    xlabel('Distance (\mum)')
    ylabel('Concentration (nM)')
    axis([0 x_f 0 L0])
    function dy = odefcn(x,y,D_ij,k_1)
    C_L    = y(1);
    dC_Ldx = y(2);
    R_L = -k_1.*C_L;
    dy = zeros(2,1);
    dy(1) = dC_Ldx;
    dy(2) = (-R_L/D_ij);
    end
    function res = twobc(ya,yb)
    res = [ ya(1)-(L0); yb(2) ];
    end
    end