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/* Copyright: Ira W. Snyder
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/* Copyright: Ira W. Snyder
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 * Start Date: 2005-11-28
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 * Start Date: 2005-11-28
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 * End Date:
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 * End Date: 2005-11-29
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 * License: Public Domain
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 * License: Public Domain
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 *
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 *
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 * Changelog Follows:
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 * Changelog Follows:
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 * 2005-11-28
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 * 2005-11-28
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 * - Implement eval_euler() and eval_trapezoid().
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 * - Implement eval_euler() and eval_trapezoid().
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 * - Implement eval_romberg() and eval_simpson().
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 * - Implement eval_romberg() and eval_simpson().
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 *
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 *
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 */
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 */
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#include <cmath>
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#include <cmath>
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#include <cstdlib>
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#include <cstdio>
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#include <cstdio>
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#include <iostream>
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using namespace std;
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using namespace std;
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/**
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/**
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 * The function given in the Project #5 Handout.
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 * The function given in the Project #5 Handout.
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 * This is 1 + x^28
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 * This is 1 + x^28
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int main (void)
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int main (void)
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{
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{
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    const float a = 0.0;
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    const float a = 0.0;
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    const float b = 3.0;
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    const float b = 3.0;
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    const float real = 3.0 + (pow(3.0, 29.0) / 29.0);
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    float h, comp, abs, rel;
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    int n = 0;
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    int i, n;
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    /* Euler Method Header */
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    printf ("Euler's Method\n");
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    printf ("n       h               Computed        Abs Error       Rel Error\n");
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    printf ("====================================================================\n");
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    /* Euler Method Table */
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    for (n=1; n<=25; n++)
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    {
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        h = (b - a) / n;
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        comp = eval_euler (a, b, n, &func);
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        abs = fabs(real - comp);
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        rel = fabs(real - comp) / fabs(real);
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        printf ("%.2d\t%e\t%e\t%e\t%e\n", n, h, comp, abs, rel);
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    }
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    /* Trapezoid Method Header */
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    printf ("\n\nTrapezoid Method\n");
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    printf ("n       h               Computed        Abs Error       Rel Error\n");
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    printf ("====================================================================\n");
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    /* Trapezoid Method Table */
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    for (n=1; n<=25; n++)
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    {
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        h = (b - a) / n;
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        comp = eval_trapezoid (a, b, n, &func);
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        abs = fabs(real - comp);
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        rel = fabs(real - comp) / fabs(real);
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        printf ("%.2d\t%e\t%e\t%e\t%e\n", n, h, comp, abs, rel);
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    }
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    /* Romberg Method Header */
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    printf ("\n\nRomberg's Method\n");
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    printf ("n       h               Computed        Abs Error       Rel Error\n");
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    printf ("====================================================================\n");
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    /* Romberg Method Table */
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    for (n=1; n<=25; n++)
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    {
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        h = (b - a) / n;
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        comp = eval_romberg (a, b, n, &func);
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        abs = fabs(real - comp);
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        rel = fabs(real - comp) / fabs(real);
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        printf ("%.2d\t%e\t%e\t%e\t%e\n", n, h, comp, abs, rel);
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    }
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    /* Simpson Method Header */
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    printf ("\n\nSimpson's Method\n");
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    printf ("n       h               Computed        Abs Error       Rel Error\n");
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    printf ("====================================================================\n");
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    /* Simpson Method Table */
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    for (n=1; n<=25; n++)
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    {
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        h = (b - a) / n;
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        comp = eval_simpson (a, b, n, &func);
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        abs = fabs(real - comp);
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        rel = fabs(real - comp) / fabs(real);
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        printf ("%.2d\t%e\t%e\t%e\t%e\n", n, h, comp, abs, rel);
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    }
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    return 0;
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    return 0;
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}
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}
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