In the course of solving a boundary value problem for some function c(x) using centered finite differences, there is a subfunction for computing the residuals that has the following structure:

Answer the following questions about this problem.

(a) If x₁ = 0, what is x_n?

(b) What is the ordinary differential equation solved by this program?

(c) What are the boundary conditions?

(d) Write a subfunction that takes the vector c as its input and returns the Jacobian needed for the Newton–Raphson solution of the problem.

Transcribed Image Text:

1 function out = problem6_13 2 n = length (c); 3 dx = 2/(n-1); R(1,1)= c(1) for i = 2:n-1 4 5 6 7 8 9 1; out = R(1, 1) = c(i+1) - 2*c (i) + c(i-1) - (dx)^2*c (i) ^2; end R(n,1) = 2*c (n-1) + 2* (dx-1) *c (n) -c (n) ^2*dx^2; Ri