Engineering Numerical Analysis (10626251)

Use any programming language to solve the following questions:

Problem 1: Consider isentropic supersonic flow around a sharp expansion comer. The relationship between the Mach number before the comer (i.e., M₁) and after the comer (i.e., M₂), derived by Zucrow and Hoffman, is given by:

=b12tan-1M22-1b1/2-tan-1M12-1b1/2-tan-1M22-11/2- tan-1M12-11/2

b=+1-1

where is the specific heat ratio of the gas and equals to 1.4.

Use the false-position method to find the value of M₂ when M₁ = 1.5 and =10 degree.

Problem 2: Find the intersection point of the following functions, using Newton-Raphson method:

f1x,y=x-13+0.512y

f2x,y=x-2xy

Note: Your program should allow the use of any interval or starting points. However, it should indicate if the interval is valid (for Bracketing method) or if the function diverges for the given starting point (for open domain methods).