Department of Chemical EngineeringUniversity of California, Santa BarbaraChemical Engineering132BComputational Methodsin Chemical EngineeringFall 2011Homework #4Homework due: Friday, 28 October 20111. Suppose 3 moles of chemical A, 2 moles of chemical B, and 1 mole of chemical D are injected into aone-liter reaction chamber and the coupled chemical reactionsA+ 2B2C2A+DCare allowed to proceed to equilibrium. The equilibrium constants for the reactions areK1= 0.0100andK2= 0.0512. Use the multi-dimensional Newton method to find how many moles of A, B, C, andD are present at equilibrium to three significant figures. (Don’t use a built-inMatLabfunction forthis; write your own program. You can use theMatLabbackslash operator, however, for solving thelinear system at each iteration step.)2. Employ the following methods to find the maximum off(x) = 4x-1.8x2+ 1.2x3-0.3x4to a fractional relative error of 0.001(a) Newton’s method withx0= 3.
This is the end of the preview.
access the rest of the document.