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  1. #include <iostream>
  2. #include <cmath>
  3.  
  4. using namespace std;
  5.  
  6. double f(double t, double x) {
  7.     return x + exp(t) + t*x;
  8. }
  9.  
  10. int main() {
  11.     double x = 2.0;
  12.     double t = 1.0;
  13.     double h = 0.01;
  14.     double x1, x2, x3;
  15.  
  16.     // Taylor series method of order 5
  17.     for (int i = 1; i <= 200; i++) {
  18.         x1 = x + h*f(t, x) + (h*h/2.0)*((t*t*x) + (t*x) + x + exp(t));
  19.         x2 = x + h*f(t+h/2.0, x+h*f(t,x)/2.0) + (pow(h, 2)/4.0)*(2*t*x + 2*x*exp(t+h/2.0) + pow(t, 2)*x + t + exp(t+h/2.0));
  20.         x3 = x + h*f(t+h/2.0, x2/2.0 + x/2.0) + (pow(h, 2)/4.0)*(2*t*x2 + 2*x2*exp(t+h/2.0) + pow(t, 2)*x2 + t + exp(t+h/2.0));
  21.         x = x + (h/6.0)*(f(t,x) + 2*f(t+h/2.0, x+h*f(t,x)/2.0) + 2*f(t+h/2.0, x2/2.0 + x/2.0) + f(t+h,x3));
  22.         t += h;
  23.     }
  24.     cout << "The value of x at t=3 using Taylor series method of order 5 is: " << x << endl;
  25.  
  26.     // One-step Taylor series method at x=3
  27.     double x_one_step = x + h*f(t,x);
  28.     cout << "The value of x at t=3 using one-step Taylor series method is: " << x_one_step << endl;
  29.  
  30.     return 0;
  31. }
  32.  
Success #stdin #stdout 0.01s 5424KB
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Standard input is empty
stdout
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The value of x at t=3 using Taylor series method of order 5 is: 1521.82
The value of x at t=3 using one-step Taylor series method is: 1582.89
https://ideone.com/rI5dGa
language:
C++14 (gcc 8.3)
created:
1 year ago
visibility:
public

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