Advanced Numerical Method

oynpxen1a
timer Asked: Nov 16th, 2015

Question Description

Hello,

 Written code in Matlab or Fortran. I need you to answer all question completely. Thank you.

Homework4_Fall15.pdf 

Unformatted Attachment Preview

Homework 4, Advanced Numerical Methods for Engineers, Fall 2015 (due 24 November) 1. The transverse deformation of a thin elastic inextensional rod subjected to an axial loading and clamped at its end (see figure below) is governed by the following ordinary differential equation (ODE) boundary value problem (BVP): 𝑑2𝜃 + 𝑃 sin 𝜃 = 0, 𝑑𝑠 2 0< 𝑠 0 with initial condition 𝑥 (0) = 𝐴 and where 𝑘 is the spring constant. The oscillating exact solution can be taken as 𝑥 (𝑡) = 𝐴 cos(𝜔𝑡) where frequency is 𝜔 = √𝑘/𝑚 and the period of oscillation is 𝑇 = 2𝜋/𝜔. Solve the initial value problem above with 𝐴 = 𝑘 = 𝑚 = 1 (and thus 𝑇 = 2𝜋) using (a) leap frog, (b) implicit Euler and (c) explicit Euler methods with a time a time step ∆𝑡 = 0.002 𝑇. Solve the equation and plot solutions through 𝑡 = 10 𝑇. Compare the solutions with the three numerical methods to the exact solution and discuss the results while considering the results of problem 1 in homework 3. Homework 4, Advanced Numerical Methods for Engineers, Fall 2015 (due 24 November) 1. The transverse deformation of a thin elastic inextensional rod subjected to an axial loading and clamped at its end (see figure below) is governed by the following ordinary differential equation (ODE) boundary value problem (BVP): 𝑑2𝜃 + 𝑃 sin 𝜃 = 0, 𝑑𝑠 2 0< 𝑠 0 with initial condition 𝑥 (0) = 𝐴 and where 𝑘 is the spring constant. The oscillating exact solution can be taken as 𝑥 (𝑡) = 𝐴 cos(𝜔𝑡) where frequency is 𝜔 = √𝑘/𝑚 and the period of oscillation is 𝑇 = 2𝜋/𝜔. Solve the initial value problem above with 𝐴 = 𝑘 = 𝑚 = 1 (and thus 𝑇 = 2𝜋) using (a) leap frog, (b) implicit Euler and (c) explicit Euler methods with a time a time step ∆𝑡 = 0.002 𝑇. Solve the equation and plot solutions through 𝑡 = 10 𝑇. Compare the solutions with the three numerical methods to the exact solution and discuss the results while considering the results of problem 1 in homework 3.
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Related Tags

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors