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Euler Code for Project 1.4 - Varun and Shaurya

a guest Apr 22nd, 2019 105 Never
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1. funcprot(0);
2. clc();
3. clf();
4.
5. initialX = 0;
6. initialY = 550315.7725;
7. stepSize = 1;
8. numberIterations = 300;
9. colorVar = 3;
10. solFind = 260; //time at which you want to find the population
11.
12. function [dy] = f(x, y)
13.     dy = 0.02808621325311*y*(1-y/21172402.245108);
14. endfunction
15.
16. function [x, y] = euler(f, x1, y1, h, n, l)
17.     x(1) = x1;
18.     y(1) = y1;
19.     for i = 1:n
20.         x(i + 1) = x(i) + h;
21.         y(i + 1) = y(i) + h * f(x(i), y(i))
22.     end
23. plot2d(x, y, style = l+3);
24. disp(y(solFind),  " is ", solFind,"Approximation at t = ");
25. xgrid();
26. endfunction
27.
28. function [a, b, q] = actual(f, x1, y1, h, n, c)
29.     for i =1:n
30.         a(i) = h * i;
31.         b(i) = ode(y1, x1, h*i, f);
32.     end
33. plot2d(a, b, style = c);
34. disp(b(solFind),  " is ", solFind,"Actual value at t = ");
35. xtitle("Population of New York versus time");
36. xlabel("Time");
37. ylabel("Population");
38. legend('Euler approximation', 'Exact solution', 2);
39. endfunction
40.
41. euler(f, initialX, initialY, stepSize, numberIterations, colorVar);
42. actual(f, initialX, initialY, stepSize, numberIterations, colorVar);
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