How to write a code for varying step size ?

Hi! I'm working on boundary layer theory.I've written a code for solving block tri-diagonal matrix.One of the variable i've taken with variable step size to get a good accuracy.Have used if loop .While executing it takes the first if condition and executes for the whole interval as my initialization is 0.As my incremental value is the varying parameter how to bring it?

x_bar=0;
        if x_bar<=0.5 
          delx_bar=0.01;
        elseif x_bar >=0.5 && x_bar <=1.25
            delx_bar=0.005;
         else
            delx_bar=0.0001;
        end
%%Intial profiles start
x_bar=0:delx_bar:1.25;
n_xbar=length(x_bar);

As I've used x_bar and length of x_bar in the code for calculation of values i need to define it. What changes do I have to make so that my x_bar values are generated first and then the successive delx_bar are taken for calculation of values.

[James Tursa]

What do you want for a result? A vector x_bar that starts at 0, then grows by 0.01 until it reaches the value 0.5, then grows by the value 0.005 until it reaches the value 1.25, then grows by 0.0001 until it reaches some final value?

Answer 1

[Andrei Bobrov]

Xb = [0, .5, 1.25, 2];
dx = [.01, .005, .0001];
x_bar = cumsum([Xb(1), repelem(dx,diff(Xb)./dx)]);

>> x_bar_j = 1.589
delx_bar_j = dx(discretize(x_bar_j,Xb))
x_bar_j =
        1.589
delx_bar_j =
       0.0001
>>

[revathy M]

Thank you.

[Andrei Bobrov]

Hi Revathy!

If this answer solve problem from your question, please, "accept" him.

Answer 2

[James Tursa]

Does this do what you want? (Using arbitrary final value of 2.000 for example)

xstart = 0.000; xend = 0.500;  dx = 0.01;
part1 = linspace(xstart   ,xend,round((xend-xstart)/dx)+1);
xstart = 0.500; xend = 1.250;  dx = 0.005;
part2 = linspace(xstart+dx,xend,round((xend-xstart)/dx)  );
xstart = 1.250; xend = 2.000;  dx = 0.0001;
part3 = linspace(xstart+dx,xend,round((xend-xstart)/dx)  );
x_bar = [part1,part2,part3];

[revathy M]

Hi! I did try this.If i use this I will be able to get the different values of x_bar but i need the value of delx_bar in my calculation. Like

Gx_bar(1,1)=1/delx_bar;
G_eta(1,1)=-1/del_eta;
fx_bar(1,1)=f(1,1)/delx_bar;
Fx_bar(1,1)=F(1,1)/delx_bar;
Gx_bar(1,1)=G(1,1)/delx_bar;
F_eta(1,1)=F(1,1)/(2*del_eta);

These values have to be evaluated at different positions based on the values of x_bar.Also need the length of x_bar based on which the entire code has been constructed.

n_xbar=length(x_bar);
for j=2:n_xbar-1
    calculations
end

[James Tursa]

Add some code to keep track of the dx stuff:

part1 = etc.
part1x = dx*ones(size(part1));
   :
part2 = etc.
part2x = dx*ones(size(part2));
   :
part3 = etc.
part3x = dx*ones(size(part3));
   :
delx_bar = [part1x,part2x,part3x];

Then in your calculations, index into it the same way you index into x_bar. I.e., you would be using x_bar(j) and delx_bar(j) in the loop.

[revathy M]

Hi! Thank you. Will try .

[revathy M]

Hi! What's the difference between the above two syntax?

Answer 3

[Suganthi D]

Hi professor , a very happy morning. I have written a code for step input variation for 10 houses ..Time for 24 hours. But i do not is this correct or not.. I need your help .. Here I have attached the code .. I want the graph for 10 houses step variation at 24 hours.. how to write the code for tis one..

T=1:1:24; %hours

input = createStep('StepTime',5,'StepSize',5,'FinalTime',25)

plot(input);

Answer 4

[AKASH KUMAR]

clc
clear
close all

%% Variable step size

Step_0=2;
Step=Step_0;
ii=1;theta=0;
while true
    theta= theta+Step;
   th(ii)=(theta);
   Y(ii)=sind(th(ii));
   if Y(ii)>0.7 || Y(ii) <-0.7
       Step=1/10*Step_0;
   else
       Step=Step_0;
   end
   ii=ii+1;
   if theta>180*2
       break
   end
end
plot(th,Y,'.')
grid on;
xlabel('theta(deg)');

[Janet onoja]

I having been trying to get code on variable step size using adams method but I can't. Any help please.