using matlab write separate function bwdEulerFPI present figure with backward Euler approximation and exact solution to

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using matlab
write separate function bwdEulerFPI
present figure with backward Euler approximation and exact
solution to IVP
add legend

Using Matlab Write Separate Function Bwdeulerfpi Present Figure With Backward Euler Approximation And Exact Solution To 1 (153.19 KiB) Viewed 29 times

For this problem, you will build a Matlab function that will implement backward Euler's method by solving (approximately) a fixed-point problem at every step. On a separate file, write the function with definition function [w] = budEulerFPI(f, a, b, b, tol) a which should have the following: a, b Input 1 : the source term of the ODE ft,y), function of two variables • the left and right boundary of the domain of t respectively : the spacing of evenly-spaced nodes to be used in [a, b], including a and b • the tolerance to be used for the stopping condition of fixed-point iteration (see details below) Output v : the backward Euler's approximations to (yi) - with Wi 2 yi - y(ti), i - 0,...,n h tol The backward Euler's method for the Initial Value Problem y' ya) ft, y) ya astab is defined as wo ya Wi+1 W: + hfſti+1, 4+1), i - 0,...,n-1 Your function should evaluate Wi+1 as the approximate solution to the fixed-point problem $(x) = x, where $(x) – Wi + hf(ti+1,x) by applying fixed-point iteration with initial guess wi, and stopping condition | wu) - wil< tol. In your prob2(): Call your budEulerFPI function for the IVP y' - cosy+t), y(0) 0 0<t<1 with h - 0.1, tol - 10-6 Output: (a) Present a figure with your backward Euler approximation. (b) In the same figure, plot the exact solution of the IVP, y(t) = 2 arctant-t. (c) Add a legend to your figure.