MATLAB

The purpose of this problem is to review the application of programming in solving nonlinear equations. Consider a nonlinear algebraic equation f(r) 0 which does not have an analytical so- lution. In this case, to find the solution we can use computational methods. For example consider the following function: f (r) sin(r) To find the root of flac) 0, we can use the method of successive substitution for more details, read Dunn et al., Numerical Methods in Biomedical Engineering, page 124). In this method, we rearrange our equations into r g(r), or in the case of the example above g(z) (r) sun. In the next step we pick an initial guess To and calculate T1 g(ro) T1 If gr (To)I 1, T1 should be closer to the root than our initial guess. A general iterative formula for this method is g (rn) n+1 Let us use this method to find the roots of sin (T) 0. As stated previously g(z) sin (r) a. We set our initial guess co to be 1. The successive substitution method gives the following values for T at each iteration step sin (zo) Iteration 1 1.365069760 0.365069760 To sin (r1) Iteration 2 1.502511597 0.137441836 Iteration 3 T3 sin(r2) 1.521268279 Iz3 T2 0.018756683