MATLAB: Forward, backward and central differences

backward differencecentral differencefdiffforward differenceintegration

hey please i was trying to differentiate this function: y(x)=e^(-x)*sin(3x), using forward, backward and central differences using 101 points from x=0 to x=4. and plot the estimates and the actual function derivatives. here is my code:
f = @(x) exp(-x)*sin(3*x); %actual derivative of function fprime = @(x) -exp(-x)*sin(3*x)+ 3*exp(-x)*cos(3*x);
 %step size:
 h=0.04;
%forward difference dfdx_forward = (f(2+h)-f(2))/h Error_forward = fprime(2)-dfdx_forward %error
 %bacward difference
 dfdx_backward = (f(2)-f(2-h))/h
Error_backward = fprime(2)-dfdx_backward %error

 %central difference
dfdx_central = (f(2+h)-f(2-h))/(2*h)
Error_central = fprime(2)-dfdx_central %error
please let me know if this is right and where i made my mistakes

Best Answer

Fun = @(x) exp(-x).*sin(3*x); 
dFun = @(x) -exp(-x).*sin(3*x)+ 3*exp(-x).*cos(3*x);
x=linspace(0,4,101);
F=Fun(x);
h=x(2)-x(1);
xCentral=x(2:end-1);
dFCenteral=(F(3:end)-F(1:end-2))/(2*h);
xForward=x(1:end-1);
dFForward=(F(2:end)-F(1:end-1))/h;
xBackward=x(2:end);
dFBackward=(F(2:end)-F(1:end-1))/h;
plot(x,dFun(x));
hold on
plot(xCentral,dFCenteral,'r')
plot(xForward,dFForward,'k');
plot(xBackward,dFBackward,'g');
legend('Analytic','Central','Forward','Backward')
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