What modifications do I need to make in the following codes for solving the boundary value problem similar to the Blasius equation using Shooting method with R-K 4 numerical analysis

The equation is (1+2M*eta)f'''+ 2Mf"+ f*f"- (f')^2- K1*f'= 0 ; f' is df/d(eta) 'eta' is a similarity variable

 where M- is a curvature parameter, M = 1

k1- is another parameter, k1= 0.1

boundary conditions are: eta=0, f(0)=0, f'(0)=1, f'(inf)=0, inf= 10

The following is the code for Blasius equation

% Fourth Runge Kutta for solving Blasius Equation

%-----------------------------------------------

%Blasius Equation : 2f"+ff'=0

%-----------------------------------------------

%Boundary Condition

%1. f'(0) = 0

%2. f'(inf) = 0

%3. f(0) = 0

%from shooting method

%4. f"(0) = 0.332

%-----------------------------------------------

%find: f,f" and f'''

%-----------------------------------------------

%Given

%eta = x

%f = y0,f'=y1,f"=y2,f'''= -(1/2)*y0*y2

%-----------------------------------------------

func1 = inline('y1','x','y0','y1','y2');

%-----------------------------------------------

func2 = inline('y2','x','y0','y1','y2');

%-----------------------------------------------

func3 = inline('-0.5*y0*y2','x','y0','y1','y2');

%-----------------------------------------------

%input: x = 0 , y0 = 0 , y1= 0

% y2 = 0.332 , total = 7 and h = 0.1

%-----------------------------------------------

x = input('\n Enter the value of x : ');

y0 = input( 'Enter the value of y0 : ');

y1 = input( 'Enter the value of y1 : ');

y2 = input( 'Enter the value of y2 : ');

total = input('Enter the value of total : ');

h = input( 'Enter the value of h : ');

fprintf('\n Solution with step size =%5.3f is:',h);

fprintf('\n x y0 y1 y2');

fprintf('\n%16.3f%16.3f%16.3f%16.3f',x,y0,y1,y2);

for i = 1:(total/h)

ak1y0 = func1(x,y0,y1,y2);

ak1y1 = func2(x,y0,y1,y2);

ak1y2 = func3(x,y0,y1,y2);

xx = x + h/2.;

yy0 = y0 + h*ak1y0/2.;

yy1 = y1 + h*ak1y1/2.;

yy2 = y2 + h*ak1y2/2.;

ak2y0 = func1(xx,yy0,yy1,yy2);

ak2y1 = func2(xx,yy0,yy1,yy2);

ak2y2 = func3(xx,yy0,yy1,yy2);

yy0 = y0 + h*ak2y0/2.;

yy1 = y1 + h*ak2y1/2.;

yy2 = y2 + h*ak2y2/2.;

ak3y0 = func1(xx,yy0,yy1,yy2);

ak3y1 = func2(xx,yy0,yy1,yy2);

ak3y2 = func3(xx,yy0,yy1,yy2);

all_x(i) = x;

all_y0(i) = y0;

all_y1(i) = y1;

all_y2(i) = y2;

xx = x + h;

yy0 = y0 + h*ak3y0;

yy1 = y1 + h*ak3y1;

yy2 = y2 + h*ak3y2;

ak4y0 = func1(xx,yy0,yy1,yy2);

ak4y1 = func2(xx,yy0,yy1,yy2);

ak4y2 = func3(xx,yy0,yy1,yy2);

y0 = y0 + (ak1y0 + 2.*ak2y0 + 2.*ak3y0 + ak4y0)*h/6.;

y1 = y1 + (ak1y1 + 2.*ak2y1 + 2.*ak3y1 + ak4y1)*h/6.;

y2 = y2 + (ak1y2 + 2.*ak2y2 + 2.*ak3y2 + ak4y2)*h/6.;

x = x + h;

fprintf('\n%16.3f%16.3f%16.3f%16.3f',x,y0,y1,y2);

end

plot(all_x, all_y0, 'k-', all_x, all_y1, 'b-', all_x, all_y2, 'g-')

Answer 1

[Torsten]

Use MATLAB's "bvp4c" instead of a code that you don't understand.

Best wishes

Torsten.

[naygarp]

How do I use 'bvp4c' for solving bvp using Shooting method with RK-4 numerical method?