CH ENGR 109 Quiz: Homework 4 2017
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Cbe 109 - numerical and mathematical methods in chemical and biological. Note: please include your name in the rst page, label clearly the problems and put them in right order, and staple your papers: determine the solution of the following second order ode: d2x dt2 + dx dt. = x1x2 x2(1 x2) with x1(0) = 1 and x2(0) = 1. (a) we consider the explicit euler method for numerical integration. Justify your answer. (b) is the steady-state (x1, x2) = (0, 0) stable or unstable: for the following system of nonlinear odes: dx1 dt. 1 (b) apply centered nite di erences to discretize the equation and boundary conditions. (c) show the form of all vectors and matrices needed for solution using newton"s method: consider the second order ode-bvp: d2y dx2. 2y3 = 0 with y(x = 1) = 1 and y(x = 2) = Plot the analytical and numerical solutions clearly: consider the equations:
