[SOLVED] Matlab-数值计算代写: Math 128A Programming assignment 2

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.