2021-01-07 Matlab Numerical Analysis Numerical Integration and Numerical Differential Compound Trapezoid Formula Compound Simpson Formula

Matlab numerical analysis, numerical integration and numerical differentiation

 

1 Compound trapezoidal formula

function I=ftrapz(f,a,b,n)
format long             %显示15位双精度
h=(b-a)/n;
x=linspace(a,b,n+1);
y=feval(f,x); 
I=h*(0.5*y(1)+sum(y(2:n))+0.5*y(n+1));

Function file

function y=fun1(x)y=exp(-x);

Calling program 

t=ftrapz(@fun1,0,1,10)

2 Compound Simpson formula

function I=fsimpson(fun,a,b,n)
h=(b-a)/n;
x=linspace(a,b,2*n+1);
y=feval(fun,x);
I=(h/6)*(y(1)+2*sum(y(3:2:2*n-1))+4*sum(y(2:2:2*n))+y(2*n+1));

 

Function file

function y=fun1(x)y=exp(-x);

Calling program

 

s=fsimpson(@fun1,0,1,10)