Answer Happy

Consider the boundary value problem (BVP) da da ab, a(0) = 1, (1) = 2, dra doc P- db = (a - 62), (0) = 0, 6(1) = 1. dr dr2 (a). Set up (in writing) the boundary value problem for Matlab solution using shooting method (Blackbox function approach) and Matlab function bvplc. Before writing Matlab code, provide the four coupled first order ODEs and the associated boundary conditions. The four ODEs are to be integrated from r = 0 to x = 1. Define Blackbox functions (errors or residuals) at 2 = 1 and state which of the four variables, a, da/dx, b, and db/dr, need to be guessed at x = 0. For using bvp4c, define residuals at the two boundaries (left boundary - designated by a - r = 0, right boundary - designated by b - 1 = 1). No Matlab effort is required for this part. (b). Obtain the Matlab solution to the BVP using EITHER the function bvple OR the Blackbox function approach (BUT NOT BOTH). If using bvple, define the four residuals corresponding to the four boundary conditions and four arbitrary guess profiles for a, da/dx, b, and db/dx. If using Blackbox function, you must work with guesses for da/dx and b at 1 = 0 and Blackbox functions corresponding to boundary conditions at r=1. The guesses at x = 0 must be improved using fsolve (and not fzero) as there are two guesses. The Matlab m-file che439s1 7hw6pl.m on Blackboard in the folder S17MFiles will be very useful. Alter it appropriately for solving this problem. (e). If successful in running the Matlab code, provide plots of a and b versus r.