Question

Write a C program that numerically calculates the second derivative of the function f(t) = sin(H) + 0.3A where the input&ranges [0:0.1:5). Find the second derivative at each point not including the first and last points. Also calculate the analytical solution at each point. Print to the screen the numerical and analytical results for comparison

Answer 1

`Hey,

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#include<stdio.h>
#include<stdlib.h>
#include<math.h>
double fun(double t)
{
return sin(t*t)+0.3*t*t*t;
}
double gfun(double t)
{
return (9.0*t)/5.0+2.0*cos(t*t)-4.0*t*t*sin(t*t);
}
int main()
{
double h=1e-7;
double t;
for(t=0.1;t<5;t=t+0.1)
{
double num=(fun(t+h)-2*fun(t)+fun(t-h))/(h*h);
printf("Second derivative at t=%f, numerically is %f and analytically is %f\n",t,num,gfun(t));
}
return 0;
}

FAcheckimain.exe Second derivative at t-0.1e80e, numerically is 2.179645 and analytically is 2.179500 Second derivative at t-0.28ee0, numerically is 2.351214 and analytically is 2.352002 Second derivative at t-0.38e0, numerically is 2.501264 and analytically is 2.499549 Second derivative at t-8.488, numerically is 2.583741 and analytically is 2.592491 Second derivative at t-0.5e0, numerically is 2.581073 and analytically is 2.590421 Second derivative at t-8.688, numerically is 2.449530 and analytically is 2.444519 Second derivative at t-0.780, numerically is 2.108392 and analytically is 2.102239 Second derivative at t-0.88ee0, numerically is 1.521298 and analytically is 1.515371 Second derivative at t-0.98, numerically is 8.665332 and analytically is .652306 Second derivative at t-1.888, numerically is -0.486666 and analytically is -0.485279 Second derivative at t=1.1eeeee, numerically is -1.868488 and analytically is -1.842343 Second derivative at t=1.2eeeee, numerically is -3.300214 and analytically is -3.289953 Second derivative at t=1.3eeeee, numerically is -4.594610 and analytically is -4.689872 Second derivative at t-1.488, numerically is -5.479135 and analytically is -5.492562 Second derivative at t=1.seeeee, numerically is -5.567096 and analytically is -5.559806 Second derivative at t-1.688, numerically is -4.427448 and analytically is -4.416577 Second derivative at t=1.78eeee, numerically is -1.712356 and analytically is -1.754859 Second derivative at t=1.8eeeee, numerically is 2.483311 and analytically is 2.522978 Second derivative at t=1.9eeeee, numerically is 8.164541 and analytically is 8.154589 Second derivative at t-2.e88eee, numerically is 14.398790 and analytically is 14.401553 Second derivative at t-2.188ee0, numerically is 19.995984 and analytically is 20.024031 Second derivative at t-2.28ee0, numerically is 23.489855 and analytically is 23.417189 Second derivative at t-2.38ee0, numerically is 22.964269 and analytically is 22.95925e Second derivative at t-2.488e0, numerically is 17.491607 and analytically is 17.564213 Second derivative at t-2.58ee0, numerically is 7.405621 and analytically is 7.328379 Second derivative at t-2.688, numerically is -5.944637 and analytically is -5.953126 Second derivative at t-2.78e0, numerically is -18.627461 and analytically is -18.714979 Second derivative at t-2.888eee, numerically is -26.375126 and analytically is -26.288972 Second derivative at t-2.98, numerically is -24.437917 and analytically is -24.488201 Second derivative at t=3.eeeeee, numerically is -11.624122 and analytically is -11.258526 Second derivative at t=3.1eeeee, numerically is 10.698734 and analytically is 10.693503 Second derivative at t=3.20eeee, numerically is 34.090959 and analytically is 34.202464 Second derivative at t-3.388ee0, numerically is 49.e80531 and analytically is 49.046710 Second derivative at t=3.48eeee, numerically is 46 . 256401 and analytically is 46.257850 Second derivative at t=3.seeeee, numerically is 23.268453 and analytically is 23.445598 Second derivative at t-3.688, numerically is -11.397480 and analytically is -11.555810 Second derivative at t=3.78eeee, numerically is -41.785875 and analytically is -41.850940 Second derivative at t=3.8eeeee, numerically is -48.868722 and analytically is -48.888107 Second derivative at t=3.98eeee, numerically is -23.758620 and analytically is -23.796558 Second derivative at t-4.88e0, numerically is 23.978236 and analytically is 23.710493 Second derivative at t-4.18800, numerically is 66.394806 and analytically is 66.463218 Second derivative at t-4.28e0, numerically is 74.164459 and analytically is 74.272867 Second derivative at t-4.380, numerically is 35.749875 and analytically is 35.635567 Second derivative at t-4.400000, numerically ǐs -27.786627 and analytically IS -28. 169400 O Type here to search ENG 11:14 AM US 04/16/19

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