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Ralston's method function

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Emily Gallagher
Emily Gallagher on 7 Dec 2019
Commented: darova on 8 Dec 2019
I am trying to write a function for Ralston's method, a second order Runge Kutta method. My function does not appear to be graphing correctly in another script. Is there something wrong with my function?
function [t, y] = ralston( f, tspan, y0, n)
% ralston implement ralston method
a = tspan(1);
b = tspan(2);
h = (b - a)/n;
t = a + h*(0:n)';
y = 0*t; %vector w all elements zero
y(1) = y0;
for i = 1:n
k1 = h*f(t(i), y(i));
k2 = h*f(t(i) + 3*h/4, y(i) + 3*k1/4);
y(i+1) = y(i) + k1/3 + 2*k2/3;
end
end
  1 Comment
darova
darova on 8 Dec 2019
Can you attach function f?

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Answers (1)

Jim Riggs
Jim Riggs on 7 Dec 2019
There is an error in your function in the k2 term. For Ralstons method, it should be:
k1 = h*f(t(i), y(i));
k2 = h*( f( t(i) + 2*h/3, y(i) + 2*k1/3 ) );
  1 Comment
Jim Riggs
Jim Riggs on 7 Dec 2019
After some further review, there is also an error in y(i+1). Ralston's method should be:
k1 = h*f( t(i), y(i) );
k2 = h*f( t(i) + 2*h/3, y(i) + 2*k1/3 );
y(i+1) = y(i) + k1/4 + 3*k2/4;
or
k1 = f( t(i), y(i) );
k2 = f( t(i) + 2*h/3, y(i) + 2*h*k1/3 );
y(i+1) = y(i) + h*(k1/4 + 3*k2/4);
Also note that in order for the function to graph as expected, you must supply the correct starting value, y0.

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