# AAE512-HW-1.pdf - AAE 512 Homework 1 Due Feb 12 2021 For...

• 1

This preview shows page 1 out of 1 page.

AAE 512 Homework 1 T. Shih Due: Feb. 12, 2021 2021 Spring For all programming homework throughout this semester, please Explain in a WRITE-UP that covers (1) discretization of domain, (2) discretization of ODE or PDE, (3) solution algorithm, (4) efforts made to ensure an accurate solution (e.g., how time-step size or grid spacing were selected), and (5) discussion on results (e.g., does it make sense). Turn in WRITE-UP and Computer Program. Problem 1: 25% Use the Heun method, a 2 nd -order Runge-Kutta method, to compute the solution to the following ODE for two time steps by using hand computations with D x = 0.1 (show details of your work in a step-by- step fashion): 2 d 2 y/dx 2 + (3x 2 y) (dy/dx) = 10x 2 , where y = dy/dx = 2 at x = 1 Problem 2: 25% Use the trapezoidal implicit method, a 2 nd -order Adams-Moulton method, to compute the solution to the following ODE for two time steps by using hand computations with D x = 0.1 (show details of your work in a step-by-step fashion; when using Newton-Raphson to solve for roots, just do two iterations; use quadratic eq. solution only to check how well one or two iterations might lead to):