HELP ME SOLVE THIS ANALYTICAL SOLUTION

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Vetrichelvan Pugazendi 2018-4-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/396961-help-me-solve-this-analytical-solution

评论： Vetrichelvan Pugazendi 2018-4-24

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here's the coding that i did for part a so far

clc
clear all 
close all 
%%Parameters of Blasius Equation
U_inf = 1;
L = 10;
mu = 1.789E-5;
rho = 1.225;
nu = mu/rho;
A = sqrt(nu/U_inf);
h = 0.01;
%%Numerical Solution of Blasius Equation Using Runge-Kutta
f1 = @(x, y1, y2, y3) y2;
f2 = @(x, y1, y2, y3) y3;
f3 = @(x, y1, y2, y3) -y1*y3;
eta = 0:h:10;
x = 0:h:10;
y1(1) = 0;
y2(1) = 0;
y3(1) = 0.4696;
for i = 1:(length(eta)-1)
a = h.*[f1(eta(i), y1(i), y2(i), y3(i)), f2(eta(i), y1(i), y2(i), y3(i)), f3(eta(i), y1(i), y2(i), y3(i))];
b = h.*[f1(eta(i), y1(i)+a(1)/2, y2(i)+a(2)/2, y3(i)+a(3)/2), f2(eta(i)+h/2, y1(i)+a(1)/2, y2(i)+a(2)/2, y3(i)+a(3)/2), f3(eta(i)+h/2, y1(i)+a(1)/2, y2(i)+a(2)/2, y3(i)+a(3)/2)];
c = h.*[f1(eta(i), y1(i)+b(1)/2, y2(i)+b(2)/2, y3(i)+b(3)/2), f2(eta(i)+h/2, y1(i)+b(1)/2, y2(i)+b(2)/2, y3(i)+b(3)/2), f3(eta(i)+h/2, y1(i)+b(1)/2, y2(i)+b(2)/2, y3(i)+b(3)/2)];
d = h.*[f1(eta(i), y1(i)+c(1), y2(i)+c(2), y3(i)+c(3)), f2(eta(i)+h, y1(i)+c(1), y2(i)+c(2), y3(i)+c(3)), f3(eta(i)+h, y1(i)+c(1), y2(i)+c(2), y3(i)+c(3))];
y3(i+1) = y3(i)+ 1/6*(a(3)+2*b(3)+2*c(3)+d(3));
y2(i+1) = y2(i)+ 1/6*(a(2)+2*b(2)+2*c(2)+d(2));
y1(i+1) = y1(i)+ 1/6*(a(1)+2*b(1)+2*c(1)+d(1));
end
%%Plotting and Visualization
figure(1)
plot(eta,y1,eta, y2, eta, y3, 'LineWidth', 2)
xlim([0 10])
title('Solution of Blasius eqution', 'FontSize', 14);
xlabel('f, f'' and f''''', 'FontSize', 20);
ylabel('\eta', 'FontSize', 20);
grid on
Legend1 = {'f(\eta)', 'f''(\eta)', 'f''''(\eta)'};
legend(Legend1, 'FontSize', 14);