simpsons method in matlab

To use Simpson's Method for numerical integration in MATLAB, follow these steps:

1. Define the integrand function in MATLAB. Let's say we want to integrate the function f(x) = x^2 over the interval [0,1]. We can define this function in MATLAB as follows:

main.m
function y = f(x)
    y = x.^2;
end
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2. Define the limits of integration and the number of subintervals. For Simpson's Method, the number of subintervals must be even. We will use 4 subintervals for this example.

main.m
a = 0;
b = 1;
n = 4;
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3. Calculate the width of each subinterval.

main.m
h = (b - a) / n;
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4. Define the x-values at each subinterval.

main.m
x = a:h:b;
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5. Calculate the y-values at each subinterval using the integrand function.

main.m
y = f(x);
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6. Use Simpson's Method to estimate the integral.

main.m
I = (h/3) * (y(1) + 4*y(2) + 2*y(3) + 4*y(4) + y(5));
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7. The value of the integral for the given function and limits of integration is approximately 0.3333.

Full code sample:

main.m
function y = f(x)
    y = x.^2;
end

a = 0;
b = 1;
n = 4;
h = (b - a) / n;
x = a:h:b;
y = f(x);
I = (h/3) * (y(1) + 4*y(2) + 2*y(3) + 4*y(4) + y(5));
disp(I);
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