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// Taylor-Series_4th-order.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include <iostream>
#include <cmath>
using namespace std;
float Taylor4(float a, float xa, float b, int n);
#define dx1(t,x) (1 + pow(b, 2) + pow(a, 3)) // (a,b) = (t,x)
#define dx2(t,x,dx1) (2 * x*dx1 + 3 * pow(a, 2))
#define dx3(t,x,dx1,dx2) (2 * x*dx2 + 2 * pow(dx1, 2) + 6 * a)
#define dx4(t,x,dx1,dx2,dx3) (2 * x*dx3 + 6 * dx1*dx2 + 6)
void main()
{
float ans;
ans = Taylor4(1, -4, 2, 1); //when n=1, ans should be -987.75
cout << "Answer is:" << ans; //when n=100, ans should be 4.3712096
cin.ignore();
}
float Taylor4(float a, float xa, float b, int n) // n is the number of intervals
{
int k;
float h, x, t, fx1, fx2, fx3, fx4, ti;
t = a;
x = xa;
h = (b - a) / n;
// ti = t;
cout << "k=0" << "\t a=" << t << "\t xa=" << x << "\t h=" << h << endl;
for (k = 1; k < n + 1; k++)
{
fx1 = dx1(t, x);
fx2 = dx2(t, x, fx1);
fx3 = dx3(t, x, fx1, fx2);
fx4 = dx4(t, x, fx1, fx2, fx3);
x = x + h*(fx1 + 0.5*h*(fx2 + (1.0 / 3.0)*h*(fx3 + (float)0.25*h*fx4)));
t = t + k*h;
cout << "k=" << k << "\t a=" << t << "\t xa=" << x << "\t h=" << h << endl;
}
return (x);
}
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