ME 2016 Computing Techniques Section C- Spring 2017 Computing Project One Due Thursday, February 16th at 3:00pm Numerical Errors and Root-Finding Algorithms Please read all instructions( on 2 pages) before starting to write any code. Submission of your answers
• At the end of the class on 02 / 07, upload any Matlab code that you have written on T-Square • By 3:00 pm on Thursday 02 / 16, upload your final Matlab codes on T-Square. • At the start of the class on 02 / 16, turn in the print-out of the codes, the print-out of the outputs of your code and the graph. Problem statement A shock wave, which is an extremely thin non-equilibrium region, is caused by the collision of fast moving gas with slower moving gas( e. g., the leading edge of a supersonic wing). The following equation relates the dimensionless velocity inside the shock wave ϕ to the various parameters of the system: 1 − = [( 1 −) 1( − 0)]( −) where ξ is the dimensionless position inside the shock wave, 1 is the Mach number for the high velocity gas and α and β are constants. For = 0.32 and 1 = 2, determine ϕ at the leading edge of the shock wave( i. e. ξ = ξ0). Tasks 1. Write the equation to be solved in the form f( ϕ) = 0( for the case ξ = ξ0). Plot the function f( ϕ) as a function of ϕ to get an idea of the value of the root( you can only plot f for ϕ & gt; 0.32). 2. Write a function for the secant algorithm. The inputs should be the function f( as an anonymous function handle), the 1st initial guess x0, the 2nd initial guess x1, and the maximum allowable approximate percent relative error,. The outputs of the functions should be the value of the root, xr, the value of the approximate percent relative error,, and the