same value for first and second solution

Question

Amir 2023-11-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2049987-same-value-for-first-and-second-solution

评论： Ganesh 2023-11-29

function newfypAmir
format long g 
%Define all parameters 
global Pr A C M K SS
M = 1;
K = 1;
A = 3;
C = -12;
Pr = 0.5;
SS = 0;
%Boundary layer thickness & stepsize
etaMin = 0;
etaMax1 = 15;
etaMax2 = 12; %15, 10
stepsize1 = etaMax1;
stepsize2= etaMax2;
%%%%%%%%%%%%%%%%%%%%%%   First solution   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10); 
solinit = bvpinit (linspace (etaMin, etaMax1, stepsize1), @OdeInit1);
sol = bvp4c(@OdeBVP, @OdeBC, solinit, options);
eta = linspace (etaMin, etaMax1, stepsize1);
y = deval (sol, eta);
%Displaying the output for first solution 
fprintf('\nFirst solution:\n');
fprintf('f" = %7.9f\n',y(3));
fprintf('f` = %7.9f\n',y(2));
fprintf('theta = %7.9f\n',y(4));
fprintf('\n');
%%%%%%%%%%%%%%%%%%%%%%   Second solution   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options = bvpset('stats','off','RelTol',1e-10); 
solinit = bvpinit (linspace (etaMin, etaMax2, stepsize2), @OdeInit2);
sol = bvp4c (@OdeBVP, @OdeBC, solinit, options);
eta = linspace (etaMin, etaMax2, stepsize2);
y = deval (sol, eta);
%Displaying the output for second solution 
fprintf('\nSecond solution:\n');
fprintf('f" = %7.9f\n',y(3));
fprintf('f` = %7.9f\n',y(2));
fprintf('theta = %7.9f\n',y(4));
fprintf('\n');
%Define the ODE function
function ff = OdeBVP(~, y, Pr, M, K, A, C, SS)
global Pr M K A C SS
ff = [
    y(2)
    y(3)
    ( y(2)*y(2) - y(1)*y(3) - K*(1-y(2)) - M*M*(1-y(2)) - 1 ) / Pr
    y(5)
    -1*y(1)*y(5)     
    ];
%Define the boundary condition
function res = OdeBC(ya, yb, A, C, SS) 
global A C SS
res = [
    ya(1)-SS
    ya(2)-C-A*ya(3)
    ya(4)-1
    yb(2)-1
    yb(4)];
%Setting the initial guess for first solution  
function v = OdeInit1 (~, A, C, SS)
global A C SS
v = [0.5
    0
    0
    0
    0];
%Setting the initial guess for second solution  
function v1 = OdeInit2 (x, A, C, SS)
global A C SS
v1 = [exp(-x)
    exp(-x)   
    exp(-x)
    exp(-x)
    exp(-x)];