Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Given an initial-boundary value problem for the heat equation 1 00 16 u(0,1) = u(1,t) = 0, t20 u(x,0) = 2sin(2nx) with step size At = 0.01 and Ar=0.2. By using finite difference formula, find the equation of u;, 1 . a) b) Sketch a stencil in (x, t) plane, based on the u,obtained in (a). c) Then, find all the solutions of the initial-boundary value problem up to t = 0.01. (Show your calculations in detail).

Given an initial-boundary value problem for the heat equation 1 00 16 u(0,1) = u(1,t) = 0, t20 u(x,0) = 2sin(2nx) with step size At = 0.01 and Ar=0.2. By using finite difference formula, find the equation of u;, 1 . a) b) Sketch a stencil in (x, t) plane, based on the u,obtained in (a). c) Then, find all the solutions of the initial-boundary value problem up to t = 0.01. (Show your calculations in detail).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Given an initial-boundary value problem for the heat equation 1 u, =-u. 16 0<x<1, t> 0 u(0,t) = u(1,t) = 0, t20 u(x,0) = 2 sin(2ax) with step size At = 0.01 and Ax= 0.2. By using finite difference formula, find the equation of u41 . Sketch a stencil in (x, t) plane, based on the u, obtained in (a). a) b) Then, find all the solutions of the initial-boundary value problem up to t = 0.01. (Show your calculations in detail). c)
Transcribed Image Text:Given an initial-boundary value problem for the heat equation 1 u, =-u. 16 0<x<1, t> 0 u(0,t) = u(1,t) = 0, t20 u(x,0) = 2 sin(2ax) with step size At = 0.01 and Ax= 0.2. By using finite difference formula, find the equation of u41 . Sketch a stencil in (x, t) plane, based on the u, obtained in (a). a) b) Then, find all the solutions of the initial-boundary value problem up to t = 0.01. (Show your calculations in detail). c)
Expert Solution
steps

Step by step

Solved in 5 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS