Math 128A, Fall 2016.
Programming assignment 2, due Dec 4th. 1. Consider a combustion-type equation:
dy =ay2(1−y). dt
Develop a MATLAB function Euler.m to solve this equation using the Euler method of the form
function [ylast] = Euler(t0,y0,tlast,N,a)
-
% t0: initial value of t
-
% y0: initial value of y
-
% tlast: final value of t
-
% ylast: final value of y
-
% N: number of steps in Euler scheme
-
% a: parameter of the problem
Your program may not use any of the MATLAB built-in functions for solving ODEs.
2. Develop a MATLAB function RungeKutta.m that solves the same equation using the Runge-Kutta 4 method; the function should be of the form
function [ylast] = RungeKutta(t0,y0,tlast,N,a)
% t0, y0, tlast, ylast, N,a: same as above
Your program may not use any of the MATLAB built-in functions for solving ODEs.
3. Solve the same equation with t0 = 0, y0 = 0.6, a = 1 “by hand” exactly. Plot its exact solution on the interval [0, 2000] against its solutions found by Euler.m and RungeKutta.m on the same interval for N = 10, N = 100, N = 1000, N = 10000.